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Based on the study of non-invertible symmetries, we propose there exist infinitely many new renormalization group flows between Virasoro minimal models $\mathcal{M}(kq + I, q) \to\mathcal{M}(kq-I, q)$ induced by $\phi_{(1,2k+1)}$. They vastly generalize the previously proposed ones $k=I=1$ by Zamolodchikov, $k=1, I>1$ by Ahn and L\"assig, and $k=2$ by Dorey et al. All the other $\mathbb{Z}_2$ preserving renormalization group flows sporadically known in the literature (e.g. $\mathcal{M}(10,3) \to \mathcal{M}(8,3)$ studied by Klebanov et al) fall into our proposal (e.g. $k=3, I=1$). We claim our new flows give a complete understanding of the renormalization group flows between Virasoro minimal models that preserve a modular tensor category with the $SU(2)_{q-2}$ fusion ring., Comment: 30 pages, 6 tables, 2 figures, v2: reference added

But if you treat it as a two-form, you get three nontrivial renormalization group fixed points! Which becomes the Heisenberg fixed point in three dimensions? Motivated by this question, we study the conformal bootstrap constraint in the $O(d)$ anti-symmetric matrix model in $d$ dimensions, varying $d$ as a continuous parameter. Besides the one that is naturally connected to the Heisenberg fixed point in three dimensions, we find "evanescent" kinks whose origin is yet to be identified. We also bootstrap $O(4), O(5), O(6)$ anti-symmetric matrix model in $d=3$, aiming at physical applications., Comment: 28 pages, 12 figures; v2: a plot and reference added, minor corrections

Can space-time symmetries such as Lorentz, dilatation, or conformal symmetry be recovered at infinite temperature? To address this question, we study correlation functions of generalized free conformal field theories (a.k.a free holographic theories in thermal AdS space-time) at infinite temperature. We show that they are broken at the leading order in bosonic correlation functions, but a non-trivial scaling symmetry may emerge., Comment: 8 pages

In the Einstein-Maxwell-charged scalar system with a negative cosmological constant in arbitrary dimensions higher than three, there exists a horizonless charged soliton solution, which we construct explicitly for an arbitrary mass of the scalar in perturbative series in small charge. We find that the stability of the soliton is determined by the validity of the AdS weak gravity conjecture. The existence of a stable soliton might endanger the convexity of the (free) energy as a function of the charge because the phase transition between the soliton and the extremal Reissner-Nordstrom black hole would be discontinuous. We, however, argue that the existence of the hairy black hole solution circumvents the violation of convexity. The thermodynamic properties of the hairy black hole show that the phase transition becomes continuous irrespective of whether the AdS weak gravity conjecture holds. When it holds, the phase transition occurs between the soliton and the hairy black hole, and when it is violated, the phase transition occurs between the extremal Reissner-Nordstrom black hole and the hairy black hole., Comment: 41 pages, 1 figure

We discuss the possibility of a central extension of the Poincar\'e algebra and the scaling Poincar\'e algebra. In more than two space-time dimensions, all the central extensions are trivial and can be removed. In two space-time dimensions, both the Poincar\'e algebra and the scaling Poincar\'e algebra have distinct non-trivial central extensions that cannot be removed. In higher dimensions, the central charges between dilatation and global $U(1)$ symmetry may not be removed. Based on these central extensions, we give some examples of projective representations of the (scaling) Poincar\'e symmetry in two dimensions., Comment: In memory of Roman Jackiw, 9 pages, v2: reference added

A dipolar fixed point introduced by Aharony and Fisher is a physical example of interacting scale-invariant but non-conformal field theories. We find that the perturbative critical exponents computed in $\epsilon$ expansions violate the conformal bootstrap bound. We formulate the functional renormalization group equations a la Wetterich and Polchinski to study the fixed point. We present some results in three dimensions within (uncontrolled) local potential approximations (with or without perturbative anomalous dimensions)., Comment: 15 pages

We revisit critical phenomena in isotropic ferromagnets with strong dipolar interactions. The corresponding RG fixed point - dipolar fixed point - was first studied in 1973 by Aharony and Fisher. It is distinct from the Heisenberg fixed point, although the critical exponents are close. On the theoretical side, we discuss scale invariance without conformal invariance realized by this fixed point. We elucidate the non-renormalization of the virial current due to a shift symmetry, and show that the same mechanism is at work in all other known local fixed points which are scale but not conformal invariant. On the phenomenological side, we discuss the relative strength of dipolar and short-range interactions. In some materials, like the europium compounds, dipolar interactions are strong, and the critical behavior is dipolar. In others, like Fe or Ni, dipolar interactions are weaker, and the Heisenberg critical behavior in a range of temperatures is followed by the dipolar behavior closer to the critical point. Some of these effects have been seen experimentally., Comment: 28 pages + 15 pages appendix, 2 figures

We study a higher group analog of the Weyl symmetry in four-dimensional quantum field theories. A typical example is that the modified transformation of the 2-form background gauge field replaces the operator-valued Weyl anomaly associated with gauging the 0-form global symmetry. It is analogous to the 2-group global symmetry where the modified transformation of the 2-form background gauge field replaces the operator-valued chiral anomaly associated with gauging the 0-form symmetry. The physical origin of the higher group Weyl symmetry is that under the renormalization group flow, the conserved current mixes with the electromagnetic current that couples with the dynamical gauge field. We can express these effects in the local renormalization group equations in a unified manner., Comment: 12 pages

Using the ambitwistor string theory, we study graviton scattering amplitudes in a light-like linear dilaton background of ten-dimensional supergravity. At the tree level, we find that the three-graviton amplitude coincides with the type II superstring theory, and the four or more graviton amplitudes differ from the superstring theory but satisfy the scattering equations. Due to a modified momentum conservation law different at each order in genus expansion, a non-zero amplitude is determined solely from the particular order in perturbation theory without further corrections., Comment: 10 pages, v2: some clarification added

The Nelson-Seiberg theorem dictates conditions for the spontaneous breaking of the supersymmetry in Wess-Zumino models with generic, possibly non-renormalizable, superpotential; the existence of the R-symmetry is necessary while the spontaneous breaking of the R-symmetry is sufficient. If we restrict ourselves to generic but renormalizable theories, however, there exist Wess-Zumino models whose vacua break the R-symmetry spontaneously while preserving the supersymmetry. The classification and conditions of such renormalizable exceptions are under active study. We give some new examples of spontaneous breaking of the R-symmetry with preserved supersymmetry that are not covered in the literature., Comment: 10 pages, v2: reference updated

This paper experimentally demonstrates 512 color shift keying (CSK) signal transmission for optical camera communication (OCC). We achieved error-free operation with a CMOS image sensor module and a multi-label classification neural network-based equalizer.

We investigate the fate of the non-supersymmetric Gross-Neveu-Yukawa fixed point found by Fei et al in $4-\epsilon$ dimensions with a two-component Majorana fermion continued to two dimensions. Assuming that it is a fermionic minimal model which possesses a chiral $\mathbb{Z}_2$ symmetry (in addition to fermion number parity) and just two relevant singlet operators, we can zero in on four candidates. Assuming further that the least relevant deformation leads to the supersymmetric Gross-Neveu-Yukawa fixed point (i.e. fermionic tricritical Ising model), we can rule out two of them by matching the spin contents of the preserved topological defect lines. The final candidates are the fermionic $(11,4)$ minimal model if it is non-unitary, and the fermionic $(E_{6}, A_{10})$ minimal model if it is unitary. If we further use a constraint from the double braiding relation proposed by one of the authors, the former scenario is preferable., Comment: 24 pages + Appendices; v2: version accepted by JHEP

We construct a Weyl transverse diffeomorphism invariant theory of teleparallel gravity by employing the Weyl compensator formalism. The low-energy dynamics has a single spin two gravition without a scalar degree of freedom. By construction, it is equivalent to unimodular gravity (as well as Einstein's general relativity with an adjustable cosmological constant) at the non-linear level. Combined with our earlier construction of a Weyl transverse diffeomorphism invariant theory of symmetric teleparallel gravity, unimodular gravity is represented in three alternative ways., Comment: 16 pages

In two-dimensional string theory, a probe D0-brane does not see the black hole singularity due to a cancellation between its metric coupling and the dilaton coupling. A similar mechanism may work in the Schwarzschild black hole in large $D$ dimensions by considering a suitable wrapped membrane. From the asymptotic observer, the wrapped membrane looks disappearing into nothing while the continuation of the time-like trajectory beyond the singularity suggests that it would reappear as an instantaneous space-like string stretching from the singularity. A null trajectory can be extended to a null trajectory beyond the singularity. Not only the effective particle but an effective string from the wrapped membrane can exhibit the same feature., Comment: 14 pages, 1 figure

Communication in extreme environments is an important research topic for various use cases including environmental monitoring. A typical example is underwater acoustic communication for 6G mobile networks. The major challenges in such environments are extremely high-latency and high-error rate. They make real-time image transmission difficult using existing communication protocols. This is partly because frequent retransmission in noisy networks increases latency and leads to serious deterioration of real-timeness. To address this problem, this paper proposes a stochastic image transmission with Constrained Application Protocol (CoAP) for extreme environments. The goal of the proposed idea is to achieve approximate real-time image transmission without retransmission using CoAP over UDP. To this end, an image is divided into blocks, and value is assigned for each block based on the requirement. By the stochastic transmission of blocks, the reception probability is guaranteed without retransmission even when packets are lost in networks. We implemented the proposed scheme using Raspberry Pi 4 to demonstrate the feasibility. The performance of the proposed image transmission was confirmed from the experimental results.

Old folklore says that there is no non-trivial renormalization group fixed point with $U(1)$ gauge symmetry in four dimensions, but it can be circumvented by the existence of magnetic monopoles. We propose to construct (potentially infinitely many) novel types of field theories with $U(1)$ gauge symmetry by gauging $U(1) \times U(1)$ global symmetry electrically and magnetically. If the construction is consistent, the resulting theory will most likely possess a non-trivial renormalization group fixed point for the $U(1)$ gauge coupling constant and it will be a non-trivial conformal field theory without the $U(1)\times U(1)$ global symmetry in the infrared upon tunings of other relevant deformations. If the construction is CP-violating, a renormalization of the $\theta$-parameter is accompanied., Comment: 12 pages, v2 some improvement

We construct a purely fermionic system with spontaneously broken supersymmetry that shares the common feature with a fracton phase of matter. Our model is gapless due to the Nambu-Goldstone mechanism. It shows a ground-state degeneracy with the "Area-law" entropy due to fermionic subsystem symmetries. In the strongly coupled limit, it becomes a variant of the Nicolai model, and the ground-state degeneracy shows the "Volume-law" entropy. Gauging the fermionic subsystem symmetry has an t'Hooft anomaly by itself, but the would-be gauged theory may possess a fermionic defect that is immobile in certain spatial directions., Comment: 20 pages, v2: minor changes, reference added

Recent studies on swampland conjectures (e.g. non-SUSY AdS conjecture or AdS distance conjecture) predict that the (lightest) neutrino must be Dirac and the mass must be cosmologically small $m < c \Lambda^{1/4}_{\text{cc}}\sim 10 \ \text{meV}$. The Dirac neutrino naturally accompanies a $U(1)$ symmetry that can be embedded in the anomaly-free $U(1)_{B-L}$ global symmetry of the standard model. We point out that the swampland conjectures applied to a circle compactification with the $U(1)$ symmetry twisting lead to further constraints. In particular, the $U(1)$ symmetry must be broken down to $\mathbb{Z}_4$,$\mathbb{Z}_8$ or $\mathbb{Z}_{10}$ in the case of normal hierarchy, and $\mathbb{Z}_4$ in the case of inverted hierarchy, providing evidence for the absence of continuous global symmetry in quantum gravity. We also predict a more constrained upper bound of the neutrino mass for each case., Comment: 11 pages, main results appeared in master's thesis of the first author

We show that the Wess-Zumino action for the spontaneously broken Weyl (or conformal) symmetry, a.k.a dilaton effective action, in even $D$ dimensions can be obtained from the Kaluza-Klein dimensional reduction of the Lovelock action in $D+\epsilon$ dimensions by taking the $\epsilon \to 0$ limit, where the dilaton is identified with the metric in the extra dimension. The construction gives an explicit form of the dilaton effective action in any even dimensions., Comment: 10 pages, v2: reference added

We point out that the bootstrap program in quantum mechanics proposed by Han et al reduces to a bootstrap study of a microcanonical ensemble of the same Hamiltonian in the $\hbar \to 0$ limit. In the limit, the quantum mechanical archipelago becomes an extremely thin line for an anharmonic oscillator. For a double-well potential, a peninsula in $E\le 0$ appears., Comment: 5 pages; v2: some improvement in figures with new results

We construct a Weyl transverse diffeomorphism invariant theory of symmetric teleparallel gravity by employing the Weyl compensator formalism. The low-energy dynamics has a single spin two gravition without a scalar degree of freedom. By construction, it is equivalent to the unimodular gravity (as well as the Einstein gravity) at the non-linear level., Comment: 10 pages, v2: some clarification added, published version

The Gau\ss{} hypergeometric function shows a recursive structure which resembles those found in conformal blocks. We compare it with the recursive structure of the conformal block in boundary/crosscap conformal field theories that is obtained from the representation theory. We find that the pole structure perfectly agrees but the recursive structure in the Gau\ss{} hypergeometric function is slightly ``off-shell"., Comment: 10 pages

The supersymmetric Lee-Yang model is arguably the simplest interacting supersymmetric field theory in two dimensions, albeit non-unitary. A natural question is if there is an analogue of supersymmetric Lee-Yang fixed point in higher dimensions. The absence of any $\mathbb{Z}_2$ symmetry (except for fermion numbers) makes it impossible to approach it by using perturbative $\epsilon$ expansions. We find that the truncated conformal bootstrap suggests that candidate fixed points obtained by the dimensional continuation from two dimensions annihilate below three dimensions, implying that there is no supersymmetric Lee-Yang fixed point in three dimensions. We conjecture that the corresponding phase transition, if any, will be the first order transition., Comment: 18 pages, 8 figures

We show that CP-violating Weyl anomaly induces a supersymmetry anomaly in the formulation of superconformal supergravity as is observed in CP-preserving cases. This supersymmetry anomaly can be removed in the old minimal supergravity by adding suitable local counterterms, and it becomes a consistent theory., Comment: 14 pages

We investigate an alternative quantization of R-NS string theory. In the alternative quantization, we define the distinct vacuum for the left-moving mode and the right-moving mode by exchanging the role of creation operators and annihilation operators in the left-moving sector. The resulting string theory has only a finite number of propagating degrees of freedom. We show that an appropriate choice of the GSO projection makes the theory tachyon free. The spectrum coincides with the massless sector of type IIA or type IIB superstring theory without any massive excitations., Comment: 19 pages, based on the master's thesis of the first author originally in Japanese. Edited and translated by the second author

Recently a non-supersymmetric conformal field theory with an exactly marginal deformation in the large $N$ limit was constructed by Chaudhuri-Choi-Rabinovici. On a non-supersymmetric conformal manifold, $c$ coefficient of the trace anomaly in four dimensions would generically change. In this model, we, however, find that it does not change at the first non-trivial order given by three-loop diagrams., Comment: 5 pages, 1 figure

The Internet of Things (IoT) has been growing rapidly in recent years. With the appearance of 5G, it is expected to become even more indispensable to people's lives. In accordance with the increase of Distributed Denial-of-Service (DDoS) attacks from IoT devices, DDoS defense has become a hot research topic. DDoS detection mechanisms executed on routers and SDN environments have been intensely studied. However, these methods have the disadvantage of requiring the cost and performance of the devices. In addition, there is no existing DDoS mitigation algorithm on the network edge that can be performed with the low-cost and low performance equipments. Therefore, this paper proposes a light-weight DDoS mitigation scheme at the network edge using limited resources of inexpensive devices such as home gateways. The goal of the proposed scheme is to simply detect and mitigate flooding attacks. It utilizes unused queue resources to detect malicious flows by random shuffling of queue allocation and discard the packets of the detected flows. The performance of the proposed scheme was confirmed via theoretical analysis and computer simulation. The simulation results match the theoretical results and the proposed algorithm can efficiently detect malicious flows using limited resources., Comment: 6 pages

The world is often stricken by catastrophic disasters. On-demand drone-mounted visible light communication (VLC) networks are suitable for monitoring disaster-stricken areas for leveraging disaster-response operations. The concept of an image sensor-based VLC has also attracted attention in the recent past for establishing stable links using unstably moving drones. However, existing works did not sufficiently consider the one-to-many image sensor-based VLC system. Thus, this paper proposes the concept of a one-to-many image sensor-based VLC between a camera and multiple drone-mounted LED lights with a drone-positioning algorithm to avoid interference among VLC links. Multiple drones are deployed on-demand in a disaster-stricken area to monitor the ground and continuously send image data to a camera with image sensor-based visible light communication (VLC) links. The proposed idea is demonstrated with the proof-of-concept (PoC) implemented with drones that are equipped with LED panels and a 4K camera. As a result, we confirmed the feasibility of the proposed system.

Surface growth governed by the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than two undergoes a roughening transition from smooth to rough phases with increasing the nonlinearity. It is also known that the KPZ equation can be mapped onto quantum mechanics of attractive bosons with a contact interaction, where the roughening transition corresponds to a binding transition of two bosons with increasing the attraction. Such critical bosons in three dimensions actually exhibit the Efimov effect, where a three-boson coupling turns out to be relevant under the renormalization group so as to break the scale invariance down to a discrete one. On the basis of these facts linking the two distinct subjects in physics, we predict that the KPZ roughening transition in three dimensions shows either the discrete scale invariance or no intrinsic scale invariance., Comment: 7 pages, 4 figures; published version

We study anomalous hydrodynamics with a dyonic charge. We show that the local second law of thermodynamics constrains the structure of the anomaly in addition to the structure of the hydrodynamic constitutive equations. In particular, we show that not only the usual $E\cdot B$ term but also $E^2 -B^2$ term should be present in the anomaly with a specific coefficient for the local entropy production to be positive definite., Comment: 8 pages

There exists a certain argument that in even dimensions, scale invariant quantum field theories are conformal invariant. We may try to extend the argument in $2n + \epsilon$ dimensions, but the naive extension has a small loophole, which indeed shows an obstruction in non-linear sigma models in $2+\epsilon$ dimensions. Even though it could have failed due to the loophole, we show that scale invariance does imply conformal invariance of non-linear sigma models in $2+\epsilon$ dimension from the seminal work by Perelman on the Ricci flow., Comment: 14 pages

Based on the numerical conformal bootstrap bound, we show that the arbitrarily small Reissner-Nordstr\"om black hole in AdS space-time is inconsistent with holography unless the energy spectrum is modified quantum mechanically or it is unstable as indicated by the weak gravity conjecture., Comment: 10 pages

We show that there is a fermionic minimal model, i.e. a 1+1d conformal field theory which contains operators of half-integral spins in its spectrum, for each $c=1-6/m(m+1)$, $m\ge 3$. This generalizes the Majorana fermion for $c=1/2$, $m=3$ and the smallest $\mathcal{N}{=}1$ supersymmetric minimal model for $c=7/10$, $m=4$. We provide explicit Hamiltonians on Majorana chains realizing these fermionic minimal models., Comment: 5+4 pages, 1 figure, 2 tables; v2: explicit form of the interacting Majorana chain realizing the $m=5$ fermionic minimal model added, some discussions added, references added, published version up to formatting

In CP-violating conformal field theories in four dimensions, the Pontryagin density can appear in the Weyl anomaly. The Pontryagin density in the Weyl anomaly is consistent, but it has a peculiar feature that the parent three-point function of the energy-momentum tensor can violate CP only (semi-)locally. In this paper, we study the supersymmetric completion of the Pontryagin density in the Weyl anomaly, where the central charge $c$ effectively becomes a complex number. The supersymmetry suggests that it accompanies the graviphoton $\theta$ term associated with the R-symmetry gauging in the Weyl anomaly. It also accompanies new CP-violating terms in the R-current anomaly. While there are no conclusive perturbative examples of CP-violating super Weyl anomaly, we construct explicit supersymmetric dilaton effective action which generates these anomalies., Comment: 21 pages, typos fixed, references added

Similarly to the bosonic Liouville theory, the $\mathcal{N}=2$ supersymmetric Liouville theory was conjectured to be equipped with the duality that exchanges the superpotential and the K\"ahler potential. The conjectured duality, however, seems to suffer from a mismatch of the preserved symmetries. More than fifteen years ago, when I was a student, my supervisor Tohru Eguchi gave a beautiful resolution of the puzzle when the supersymmetry is enhanced to $\mathcal{N}=4$ based on his insight into the underlying geometric structure of the $A_1$ singularity. I will review his unpublished but insightful idea and present our attempts to extend it to more general cases., Comment: 16 pages, dedicated to the memories of Prof. Tohru Eguchi, v2: reference added

How large can anomalous dimensions be in conformal field theories? What can we do to attain larger values? One attempt to obtain large anomalous dimensions efficiently is to use the Pauli exclusion principle. Certain operators constructed out of constituent fermions cannot form bound states without introducing non-trivial excitations. To assess the efficiency of this mechanism, we compare them with the numerical conformal bootstrap bound as well as with other interacting field theory examples. In two dimensions, it turns out to be the most efficient: it saturates the bound and is located at the (second) kink. In higher dimensions, it more or less saturates the bound but it may be slightly inside., Comment: 15 pages, 5 figures, v2: reference added

We show that a critical condition exists in four dimensional scale invariant gravity given by the pure quadratic action $\beta \,C_{\mu\nu\sigma\rho} C^{\mu\nu\sigma \rho} + \alpha \,R^2$ where $C^{\mu}_{\,\,\nu \sigma \rho}$ is the Weyl tensor, $R$ is the Ricci scalar and $\beta$ and $\alpha$ are dimensionless parameters. The critical condition in a dS or AdS background is $\beta =6 \alpha$. This leads to critical gravity where the massive spin two physical ghost becomes a massless spin two graviton. In contrast to the original work on critical gravity, no Einstein gravity with a cosmological constant is added explicitly to the higher-derivative action. The critical condition is obtained in two independent ways. In the first case, we show the equivalence between the initial action and an action containing Einstein gravity, a cosmological constant, a massless scalar field plus Weyl squared gravity. The scale invariance is spontaneously broken. The linearized Einstein-Weyl equations about a dS or AdS background yield the critical condition $\beta=6\alpha$. In the second case, we work directly with the original quadratic action. After a suitable field redefinition, where the metric perturbation is traceless and transverse, we obtain linearized equations about a dS or AdS background that yield the critical condition $\beta= 6\alpha$. As in the first case, we also obtain a propagating massless scalar field. Substituting $\beta=6\alpha$ into the energy and entropy formula for the Schwarzschild and Kerr AdS or dS black hole in higher-derivative gravity yields zero, the same value obtained in the original work on critical gravity. We discuss the role of boundary conditions in relaxing the $\beta=6\alpha$ condition., Comment: 14 pages; v2: updated references

We study conformal properties of local terms such as contact terms and semi-local terms in correlation functions of a conformal field theory. Not all of them are universal observables but they do appear in physically important correlation functions such as (anomalous) Ward-Takahashi identities or Schwinger-Dynson equations. We develop some tools such as embedding space delta functions and effective action to examine conformal invariance of these local terms., Comment: 18 pages, v2 reference added

Very special $T\bar{J}$ deformations of a conformal field theory are irrelevant deformations that break the Lorentz symmetry but preserve the twisted Lorentz symmetry. We construct a holographic description of very special $T\bar{J}$ deformations. We give a holographic recipe to study the double trace as well as single trace deformations. The former is obtained from the change of the boundary condition while the latter is obtained from the change of the supergravity background., Comment: 16 pages

Pure $R^2$ gravity has been shown to be equivalent to Einstein gravity with non-zero cosmological constant and a massless scalar field. We show that the Palatini formulation of pure $R^2$ gravity is equivalent to Einstein gravity with non-zero cosmological constant as before but with no massless scalar field. This is an important new development because the massless scalar field is not readily identifiable with any known particle in nature or unknown particles like cold dark matter which are expected to be massive. We then include a non-minimally coupled Higgs field as well as fermions to discuss how the rest of the standard model fields fit into this paradigm. With Higgs field, Weyl invariance is maintained by using a hybrid formalism that includes both the Palatini curvature scalar $\mathcal{R}$ and the usual Ricci scalar $R$, Comment: 9 pages, v2: reference added

While the argument by Zamolodchikov and Polchinski suggests global conformal invariance implies Virasoro invariance in two-dimensional unitary conformal field theories with discrete dilatation spectrum, it is not the case in more general situations without these assumptions. We indeed show that almost all the globally conformal invariant differential equations in two dimensions are neither Virasoro invariant nor Weyl invariant. The only exceptions are the higher spin conservation laws, conformal Killing tensor equations and the Laplace equation of a conformal scalar., Comment: 18 pages, v2: appendix added

We study a very special class of $T\bar{J}$ deformations of conformal field theories in two dimensions. While the deformations break the Lorentz symmetry, they preserve the twisted Lorentz symmetry. The resulting theory has right-moving Virasoro as well as left-moving translation and left-moving (chiral) scale symmetry without left-moving special conformal symmetry (nor left-moving Virasoro symmetry). As in the original $T\bar{J}$ deformations, they may be regarded as an operator dependent non-local change of coordinates. We show concrete examples based on worldsheet string theory and discuss how the non-unitary nature enables us to circumvent various no-go theorems., Comment: 21 pages

Proceedings of the workshop "Boundary and Defect Conformal Field Theory: Open Problems and Applications," Chicheley Hall, Buckinghamshire, UK, 7-8 Sept. 2017., Comment: Conference proceedings of "Boundary and Defect Conformal Field Theory: Open Problems and Applications." Invited submission to Proceedings of the Royal Society A. Section 17 is a more condensed version of arXiv:1711.05049

We study holographic dual descriptions of very special conformal field theories with the T(2) symmetry. After constructing solutions in effective five dimensional Einstein gravity coupled with massive two-form fields, we uplift them to the ten dimensional type IIB supergravity, via a consistent truncation ansatz, to derive new analytical solutions in string theory. From the Kaluza-Klein ansatz in terms of the internal Sasaki-Einstein space, we obtain their field theory interpretation with concrete realizations in a large class of holographic $\mathcal{N}=1$ supersymmetric conformal field theories. Null compactification of these theories yields holographic dual descriptions of non-relativistic critical systems with translational invariance but without rotational invariance such as the ones induced from a constant electromagnetic field., Comment: 11 pages

The pure $R^2$ gravity is equivalent to Einstein gravity with cosmological constant and a massless scalar field and it further possesses the so-called restricted Weyl symmetry which is a symmetry larger than scale symmetry. To incorporate matter, we consider a restricted Weyl invariant action composed of pure $R^2$ gravity, SU(2) Yang-Mills fields and a non-minimally coupled massless Higgs field (a triplet of scalars). When the restricted Weyl symmetry is spontaneously broken, it is equivalent to an Einstein-Yang-Mills-Higgs (EYMH) action with a cosmological constant and a massive Higgs non-minimally coupled to gravity i.e. via a term $\tilde{\xi} R |\Phi|^2$. When the restricted Weyl symmetry is not spontaneously broken, linearization about Minkowski space-time does not yield gravitons in the original $R^2$ gravity and hence it does not gravitate. However, we show that in the broken gauge sector of our theory, where the Higgs field acquires a non-zero vacuum expectation value, Minkowski space-time is a viable gravitating background solution. We then obtain numerically gravitating magnetic monopole solutions for non-zero coupling constant $\tilde{\xi}=1/6$ in three different backgrounds: Minkowski, anti-de Sitter (AdS) and de Sitter (dS), all of which are realized in our restricted Weyl invariant theory., Comment: 15 pages, 3 figures; v2: one footnote and a few references added; version to appear in PRD

The Wess-Zumino consistency condition allows more exotic forms of anomalies than those we usually encounter. For example in two-dimensional conformal field theories in the curved background with space-time dependent coupling constant $\lambda^i(x)$, a $U(1)$ current could possess anomalous divergence of the form $D^\mu J_\mu = \tilde{c} R + \chi_{ij} \partial^\mu \lambda^i \partial_\mu\lambda_j + \tilde{\chi}_{ij} \epsilon^{\mu\nu} \partial_\mu \lambda^i \partial_\nu \lambda^j + \cdots $. Another example is the CP odd Pontryagin density in four-dimensional Weyl anomaly. We could, however, argue that they are impossible in conformal field theories because they cannot correspond to any (unregularized) conformally invariant correlation functions. We find that this no-go argument may be a red herring. We show that some of these impossible anomalies avoid the no-go argument because they are not primary operators, and the others circumvent it because they are realized as semi-local terms as is the case with the conformally invariant Green-Schwartz mechanism and in the higher dimensional analogue of Liouville or linear dilaton theory., Comment: 19 pages

Cohen and Glashow argued that very special conformal field theories of a particular kind (i.e. with HOM(2) or SIM(2) invariance) cannot be constructed within the framework of local field theories. We, however, show examples of local construction by using non-linear realization. We further construct linear realization from the topological twist at the cost of unitarity. To demonstrate the ubiquity of our idea, we also present corresponding holographic models., Comment: 9 pages, v2: reference added

We solve the two-point function of the lowest dimensional scalar operator in the critical $\phi^4$ theory on $4-\epsilon$ dimensional real projective space in three different methods. The first is to use the conventional perturbation theory, and the second is to impose the crosscap bootstrap equation, and the third is to solve the Schwinger-Dyson equation under the assumption of conformal invariance. We find that the three methods lead to mutually consistent results but each has its own advantage., Comment: 24 pages; v2: some references added; v3: Typos corrected

Once we put a quantum field theory on a curved manifold, it is natural to further assume that coupling constants are position dependent. The position dependent coupling constants then provide an extra contribution to the Weyl anomaly so that we may attempt to cancel the entire Weyl anomaly on the curved manifold. We show that such a cancellation is possible for constant Weyl transformation or infinitesimal but generic Weyl transformation in two and four dimensional conformal field theories with exactly marginal deformations. When the Weyl scaling factor is annihilated by conformal powers of Laplacian (e.g. by Fradkin-Tseytlin-Riegert-Paneitz operator in four dimensions), the cancellation persists even at the finite order thanks to a nice mathematical property of the $Q$-curvature under the Weyl transformation., Comment: 11 pages, v2: comments added