Search

We consider the theory of a higher-derivative (HD) real scalar field $\phi$ coupled to a complex scalar $\sigma$, the coupling of the $\phi$ and $\sigma$ being given by two types, $\lambda_{\sigma\phi}\sigma^\dagger \sigma\phi^{2}$ and $\xi_{\sigma\phi}\sigma^\dagger \sigma\left(\partial_{\mu}\phi\right)^{2}$. We evaluate $\phi$ one-loop corrections $\delta V(\sigma)$ to the effective potential of $\sigma$, both the contribution from the positive norm part of $\phi$ and that from the {\it negative norm part} (ghost). We show that $\delta V(\sigma_{\rm cl})$ at $\sigma_{\rm cl}\to \infty$, where $\sigma_{\rm cl}$ is a classical value of $\sigma$, is positive, implying the stability of $\delta V(\sigma_{\rm cl})$ by the HD 1-loop radiative corrections at high energy., Comment: 17 pages

We derive areal inequalities for five types of attractive gravity probe surfaces, which were proposed by us in order to characterize the strength of gravity in different ways including weak gravity region, taking into account of contributions of electric and magnetic charges, angular momentum, gravitational waves, and matters. These inequalities are generalizations of the Riemannian Penrose inequality for minimal surfaces, and lead to the concept of extremality for a given surface whose condition is given in terms of the gravitational mass and the electromagnetic charges. This means that the extremality is a characteristic property not only of black hole horizons or minimal surfaces but also of surfaces in weak gravity region. We also derive areal inequalities and extremality conditions for surfaces in asymptotically locally anti-de Sitter spacetimes., Comment: 23 pages

We construct the marginal loosely trapped surface (marginal LTS) for the Kerr spacetime with a small Kerr parameter perturbatively, where the LTS condition is saturated. An LTS is a surface that specifies the strong gravity region, which is a generalization of the photon sphere in the Schwarzschild spacetime. It turns out that there are an infinite number of marginal LTSs. At the leading order of the small Kerr parameter, all of the marginal LTSs have the same area. However, one can see that the maximal marginal LTS among them is uniquely determined at the higher order., Comment: 7 pages

We study new classes of metric transformations in the context of scalar-tensor theories, which involve both higher derivatives of the scalar field and derivatives of the metric itself. In general, such transformations are not invertible as they involve derivatives of the metric, which typically leads to instability due to Ostrogradsky ghosts. We show, however, that a certain class of this type of transformations is invertible: we construct new examples of invertible conformal (and also disformal) transformations with higher derivatives. Finally, we make use of these new transformations to construct extended mimetic theories of gravity, and we study their properties in the context of cosmology., Comment: 33 pages, 1 table

We investigate a gedanken experiment to destroy an extremally charged black hole by dropping a test particle, provided that there are multiple $U(1)$ gauge fields coupled with each other through higher derivative interactions. In the absence of higher derivative corrections, it is known that the Coulomb repulsion prevents a test particle that would break the extremal condition from falling into an extremal black hole and therefore the black hole cannot be destroyed. We extend this observation to include higher derivative corrections. Although the extremal condition is modified by the higher derivative interactions, we find that the repulsive force induced by the higher derivative couplings is responsible for preventing a test particle that would break the modified extremal condition to reach the event horizon. Thus, we confirm that the weak cosmic censorship conjecture holds for extremally charged black holes even in the presence of higher derivative corrections, as long as the test particle approximation is justified., Comment: 13 pages

Under certain conditions, it is shown that the positivity of the Geroch/Hawking quasi-local mass holds for the attractive gravity probe surfaces in any higher dimensions than three. We also comment on the Arnowitt-Deser-Misner mass., Comment: 7 pages

In four dimensional spacetimes with a positive cosmological constant, we introduce a new geometrical object associated with the cosmological horizon and then show the areal inequality. We also examine the attractive gravity probe surfaces as an indicator for the existence of attractive gravity., Comment: 14 pages, version accepted to PTEP

In asymptotically flat spacetimes, bearing the null geodesics reaching the future null infinity in mind, we propose new concepts, the "dark horizons" as generalizations of the photon sphere. They are defined in terms of the structure of escape/capture cones of photons with respect to a unit timelike vector field. More specifically, considering a two-sphere that represents a set of emission directions of photons, the dark horizons are located at positions where a hemisphere is marginally included in the capture and escape cones, respectively. We show that both of them are absent in the Minkowski spacetime, while they exist in spacetimes with black hole(s) under a certain condition. We derive the general properties of the dark horizons in spherically symmetric spacetimes and explicitly calculate the locations of the dark horizons in the Vaidya spacetime and the Kerr spacetime., Comment: 34 pages, 11figures, published version

In our previous papers [arXiv:2106.03150, arXiv:2110.10917, arXiv:2208.00822], we analyzed the asymptotic behavior of future directed null geodesics near future null infinity and then we showed a proposition on the accessibility of the null geodesics to future null infinity in a specific class of asymptotically flat spacetimes. In this paper, we adopt the retarded time of the Bondi coordinate as the parameter for the null geodesics and then see that one can relax the assumptions imposed in our previous studies. As a consequence, we obtain a new null-access theorem for generic asymptotically flat spacetimes., Comment: 16 pages, no figures

We show the well-posed variational principle in constraint systems. In a naive procedure of the variational principle with constraints, the proper number of boundary conditions does not match with that of physical degrees of freedom dynamical variables, which implies that, even in theories with up to first order derivatives, the minimal (or extremal) of the action with the boundary terms is not a solution of equation of motion in the Dirac procedure of constrained systems. We propose specific and concrete steps to solve this problem. These steps utilize the Hamilton formalism, which allows us to separate the physical degrees of freedom from the constraints. It reveals the physical degrees of freedom which is necessary to be fixed on boundaries, and also enables us to specify the variables to be fixed and the surface terms., Comment: 9 pages. v2: published version from PTEP, 16 pages

We obtain the matter-graviton scattering amplitude in the gravitational theory of quadratic curvature, which has $R_{\mu\nu}^2$ term in the action. Unitarity bound is not satisfied because of the existence of negative norm states, while an analog of unitarity bound for $S$-matrix unitarity holds due to the cancelation among the positive norm states and negative norm ones in the unitarity summation in the optical theorem. The violation of unitarity bound is a counter example of Llewellyn Smith's conjecture on the relation between tree-level unitarity and renormalizability. We have recently proposed a new conjecture that an analog of the unitarity bound for $S$-matrix unitarity gives the equivalent conditions to those for renormalizability. We show that the gravitational theory of quadratic curvature is a nontrivial example consistent with our conjecture., Comment: 61pages, 3 figures

A generalization of the Riemannian Penrose inequality in $n$-dimensional space ($3\le n<8$) is done. We introduce a parameter $\alpha$ ($-\frac{1}{n-1}<\alpha < \infty$) indicating the strength of the gravitational field, and define a refined attractive gravity probe surface (refined AGPS) with $\alpha$. Then, we show the area inequality for a refined AGPS, $A \le \omega_{n-1} \left[ (n+2(n-1)\alpha)Gm /(1+(n-1)\alpha) \right]^{\frac{n-1}{n-2}}$, where $A$ is the area of the refined AGPS, $\omega_{n-1}$ is the area of the standard unit $(n-1)$-sphere, $G$ is Newton's gravitational constant and $m$ is the Arnowitt-Deser-Misner mass. The obtained inequality is applicable not only to surfaces in strong gravity regions such as a minimal surface (corresponding to the limit $\alpha \to \infty$), but also to those in weak gravity existing near infinity (corresponding to the limit $\alpha \to -\frac{1}{n-1}$)., Comment: 23pages

A new sufficient condition for photons emitted near future null infinity to reach future null infinity is derived by studying null geodesics in the Bondi coordinates in asymptotically flat spacetimes. In our previous works [arXiv:2106.03150, arXiv:2110.10917], such a condition was established for photons emitted in outward or tangential directions to constant radial surfaces. This paper improves our previous result by including photons emitted in inward directions. In four dimensions, imposing the same assumptions on the metric functions as previously, we prove that photons reach future null infinity if their initial values of $|dr/du|$ are smaller than a certain quantity, where $r$ and $u$ are the radial and retarded time coordinates, respectively. This quantity is determined by the asymptotic properties of the metric and is connected to the conjectured maximal luminosity. In higher dimensions, photons emitted with $dr/du>-(1-1/\sqrt{3})\approx -0.423$ are shown to reach future null infinity without the assumptions on the metric functions., Comment: 19 pages, no figures

In accordance with current models of the accelerating Universe as a spacetime with a positive cosmological constant, new results about a cosmological upper bound for the area of stable marginally outer trapped surfaces are found taking into account angular momentum, gravitational waves and matter. Compared to previous results which take into account only some of the aforementioned variables, the bound is found to be tighter, giving a concrete limit to the size of black holes especially relevant in the early Universe., Comment: 8 pages, minor corrections, to apper in PRD

We reexamine the concept of the attractive gravity probe surface recently proposed as an indicator for strength of gravity. Then, we propose three new variant concepts and show refined inequalities for the four types of the AGPSs by taking account of the angular momentum, gravitational waves and matters., Comment: 25 pages, 2 figures

In this paper we study various dynamical aspects of the AdS/BCFT correspondence in higher dimensions. We study properties of holographic stress energy tensor by analyzing the metric perturbation in the gravity dual. We also calculate the stress energy tensor for a locally excited state on a half plane in a free scalar CFT. Both of them satisfy a reflective boundary condition that is expected for any BCFTs. We also study the behavior of the scalar field perturbation in the AdS/BCFT setup and show that they also show complete reflections. Moreover, we find that the entanglement entropy of a BCFT computed from the AdS/BCFT matched with that calculated from the Island formula, which supports the Island/BCFT correspondence in higher dimensions. Finally we show how we can calculate one point functions in a BCFT in our gravity dual., Comment: 45 + 14 pages, 11 figures

We reexamine a loosely trapped surface (LTS) proposed as an indicator for strong gravity and an attractive gravity probe surface (AGPS) as that for gravity. Refined inequalities for them are derived by taking account of angular momentum, gravitational waves and matters., Comment: 12 pages

Bearing in mind our previous study on asymptotic behavior of null geodesics near future null infinity, we analyze the behavior of geometrical quantities such as a certain extrinsic curvature and Riemann tensor in the Bondi coordinates. In the sense of asymptotics, the condition for an $r$-constant hypersurface to be a photon surface is shown to be controlled by a key quantity that determines the fate of photons initially emitted in angular directions. As a consequence, in four dimensions, such a non-expanding photon surface can be realized even near future null infinity in the presence of enormous energy flux for a short period of time. By contrast, in higher-dimensional cases, no such a photon surface can exist. This result also implies that the dynamically transversely trapping surface, which is proposed as an extension of a photon surface, can have an arbitrarily large radius in four dimensions., Comment: 17 pages, no figures, published version

We discuss a field transformation from fields $\psi_a$ to other fields $\phi_i$ that involves derivatives, $\phi_i = \bar \phi_i(\psi_a, \partial_\alpha \psi_a, \ldots ;x^\mu)$, and derive conditions for this transformation to be invertible, primarily focusing on the simplest case that the transformation maps between a pair of two fields and involves up to their first derivatives. General field transformation of this type changes number of degrees of freedom, hence for the transformation to be invertible, it must satisfy certain degeneracy conditions so that additional degrees of freedom do not appear. Our derivation of necessary and sufficient conditions for invertible transformation is based on the method of characteristics, which is used to count the number of independent solutions of a given differential equation. As applications of the invertibility conditions, we show some non-trivial examples of the invertible field transformations with derivatives, and also give a rigorous proof that a simple extension of the disformal transformation involving a second derivative of the scalar field is not invertible., Comment: 38 pages. v2: typos corrected, published version

We discuss the uniqueness of asymptotically flat and static spacetimes in the $n$-dimensional Einstein-conformal scalar system. This theory potentially has a singular point in the field equations where the effective Newton constant diverges. We will show that the static spacetime with the conformal scalar field outside a certain surface $S_p$ associated with the singular point is unique., Comment: 9 pages

We reexamine the Israel-type proof of the uniqueness theorem of the static spacetime outside the photon surface in the Einstein-conformal scalar system. We derive in a systematic fashion a new divergence identity which plays a key role in the proof. Our divergence identity includes three parameters, allowing us to give a new proof of the uniqueness., Comment: 8pages

We investigate the behavior of null geodesics near future null infinity in asymptotically flat spacetimes. In particular, we focus on the asymptotic behavior of null geodesics that correspond to worldlines of photons initially emitted in the directions tangential to the constant radial surfaces in the Bondi coordinates. The analysis is performed for general dimensions, and the difference between the four-dimensional cases and the higher-dimensional cases is stressed. In four dimensions, some assumptions are required to guarantee the null geodesics to reach future null infinity, in addition to the conditions of asymptotic flatness. Without these assumptions, gravitational waves may prevent photons from reaching null infinity. In higher dimensions, by contrast, such assumptions are not necessary, and gravitational waves do not affect the asymptotic behavior of null geodesics., Comment: 23 pages, published version, in v3 minor corrections

We examine the deSitter entropy in the braneworld model with the Gauss-Bonnet/Lovelock terms. Then, we can see that the deSitter entropy computed through the Euclidean action exactly coincides with the holographic entanglement entropy., Comment: 10pages

We define an attractive gravity probe surface (AGPS) as a compact 2-surface $S_\alpha$ with positive mean curvature $k$ satisfying $r^a D_a k / k^2 \ge \alpha$ (for a constant $\alpha>-1/2$) in the local inverse mean curvature flow, where $r^a D_a k$ is the derivative of $k$ in the outward unit normal direction. For asymptotically flat spaces, any AGPS is proved to satisfy the areal inequality $A_\alpha \le 4\pi [ ( 3+4\alpha)/(1+2\alpha) ]^2(Gm)^2$, where $A_{\alpha}$ is the area of $S_\alpha$ and $m$ is the Arnowitt-Deser-Misner (ADM) mass. Equality is realized when the space is isometric to the $t=$constant hypersurface of the Schwarzschild spacetime and $S_\alpha$ is an $r=\mathrm{constant}$ surface with $r^a D_a k / k^2 = \alpha$. We adapt the two methods of the inverse mean curvature flow and the conformal flow. Therefore, our result is applicable to the case where $S_\alpha$ has multiple components. For anti-de Sitter (AdS) spaces, a similar inequality is derived, but the proof is performed only by using the inverse mean curvature flow. We also discuss the cases with asymptotically locally AdS spaces., Comment: 28 pages, 8 figures. This version has been accepted by PTEP

We show that in the quadratic curvature theory of gravity, or simply $R_{\mu \nu} ^2$ gravity, the tree-level unitariy bound (tree unitarity) is violated in the UV region but an analog for $S$-matrix unitarity ($SS^{\dagger} = 1$) is satisfied. This theory is renormalizable, and hence the failure of tree unitarity is a counter example of Llewellyn Smith's conjecture on the relation between them. We have recently proposed a new conjecture that $S$-matrix unitarity gives the same conditions as renormalizability. We verify that $S$-matrix unitarity holds in the matter-graviton scattering at tree level in the $R_{\mu \nu} ^2$ gravity, demonstrating our new conjecture., Comment: 11 pages, 4 figures, accepted version for publication in MPLA

We study the properties of the loosely trapped surface (LTS) and the dynamically transversely trapping surface (DTTS) in Einstein-Maxwell systems. These concepts of surfaces were proposed by the four of the present authors in order to characterize strong gravity regions. We prove the Penrose-like inequalities for the area of LTSs/DTTSs. Interestingly, although the naively expected upper bound for the area is that of the photon sphere of a Reissner-Nordstroem black hole with the same mass and charge, the obtained inequalities include corrections represented by the energy density or pressure/tension of electromagnetic fields. Due to this correction, the Penrose-like inequality for the area of LTSs is tighter than the naively expected one. We also evaluate the correction term numerically in the Majumdar-Papapetrou two-black-hole spacetimes., Comment: 15 pages, 4 figures

A dynamically transversely trapping surface (DTTS) is a new concept of an extension of a photon sphere that appropriately represents a strong gravity region and has close analogy with a trapped surface. We study formation of a marginally DTTS in time-symmetric, conformally flat initial data with two black holes, with a spindle-shaped source, and with a ring-shaped source, and clarify that $\mathcal{C}\lesssim 6\pi GM$ describes the condition for the DTTS formation well, where $\mathcal{C}$ is the circumference and $M$ is the mass of the system. This indicates that an understanding analogous to the hoop conjecture for the horizon formation is possible. Exploring the ring system further, we find configurations where a marginally DTTS with the torus topology forms inside a marginally DTTS with the spherical topology, without being hidden by an apparent horizon. There also exist configurations where a marginally trapped surface with the torus topology forms inside a marginally trapped surface with the spherical topology, showing a further similarity between DTTSs and trapped surfaces., Comment: 24 pages, 15 figures, minor corrections, published version

We propose new concepts, a dynamically transversely trapping surface (DTTS) and a marginally DTTS, as indicators for a strong gravity region. A DTTS is defined as a two-dimensional closed surface on a spacelike hypersurface such that photons emitted from arbitrary points on it in transverse directions are acceleratedly contracted in time, and a marginally DTTS is reduced to the photon sphere in spherically symmetric cases. (Marginally) DTTSs have a close analogy with (marginally) trapped surfaces in many aspects. After preparing the method of solving for a marginally DTTS in the time-symmetric initial data and the momentarily stationary axisymmetric initial data, some examples of marginally DTTSs are numerically constructed for systems of two black holes in the Brill-Lindquist initial data and in the Majumdar-Papapetrou spacetimes. Furthermore, the area of a DTTS is proved to satisfy the Penrose-like inequality, $A_0\le 4\pi (3GM)^2$, under some assumptions. Differences and connections between a DTTS and the other two concepts proposed by us previously, a loosely trapped surface [arXiv:1701.00564] and a static/stationary transversely trapping surface [arXiv:1704.04637], are also discussed. A (marginally) DTTS provides us with a theoretical tool to significantly advance our understanding of strong gravity fields. Also, since DTTSs are located outside the event horizon, they could possibly be related with future observations of strong gravity regions in dynamical evolutions., Comment: 34 pages, 10 figures, figures improved, minor corrections, published version

We formulate explicitly the necessary and sufficient conditions for the local invertibility of a field transformation involving derivative terms. Our approach is to apply the method of characteristics of differential equations, by treating such a transformation as differential equations that give new variables in terms of original ones. The obtained results generalise the well-known and widely used inverse function theorem. Taking into account that field transformations are ubiquitous in modern physics and mathematics, our criteria for invertibility will find many useful applications., Comment: 5 pages

Equations of divergence type in static spacetimes play a significant role in the proof of uniqueness theorems of black holes. We generalize the divergence equation originally discovered by Robinson in four dimensional vacuum spacetimes into several directions. We find that the deviation from spherical symmetry is encoded in a symmetric trace-free tensor $H_{ij}$ on a static timeslice. This tensor is the crux for the construction of the desired divergence equation, which allows us to conclude the uniqueness of the Schwarzschild black hole without using Smarr's integration mass formula. In Einstein-Maxwell(-dilaton) theory, we apply the maximal principle for a number of divergence equations to prove the uniqueness theorem of static black holes. In higher $(n\ge 5)$ dimensional vacuum spacetimes, a central obstruction for applicability of the current proof is the integration of the $(n-2)$-dimensional scalar curvature over the horizon cross-section, which has been evaluated to be a topological constant by the Gauss-Bonnet theorem for $n=4$. Nevertheless, it turns out that the $(n-1)$-dimensional symmetric and traceless tensor $H_{ij}$ is still instrumental for the modification of the uniqueness proof based upon the positive mass theorem, as well as for the derivation of the Penrose-type inequality., Comment: v2:19 pages, typos corrected, references added, published version in CQG

We investigate the relation between the $S$-matrix unitarity ($SS^{\dagger}=1$) and the renormalizability, in theories with negative norm states. The relation has been confirmed in many theories, such as gauge theories, Einstein gravity and Lifshitz-type non-relativistic theories by analyzing the unitarity bound, which follows from the $S$-matrix unitarity and the norm positivity. On the other hand, renormalizable theories with a higher derivative kinetic term do not necessarily satisfy the unitarity bound essentially because the unitarity bound does not hold due to the negative norm states. In these theories, it is not clear if the $S$-matrix unitarity provides a nontrivial constraint related to the renormalizability. In this paper we introduce scalar field models with a higher derivative kinetic term and analyze the $S$-matrix unitarity. We have positive results of the relation., Comment: 14 pages, 2 figures

We investigate the ultraviolet (UV) behavior of two-scalar elastic scattering with graviton exchanges in higher curvature gravity theory. In the Einstein gravity, matter scattering is shown not to satisfy tree unitarity at high energy. Among a few possible directions to cure unitarity (i.e. UV completion of Einstein gravity), string theory, modified gravity, inclusion of high-mass/high-spin states, we take $R_{\mu\nu}^2$ gravity coupled to matter. We show that the matter scattering with graviton interactions satisfies the unitarity bound at high energy, in contrast with the Einstein gravity. The difference in unitarity property of the two gravity theories is due to that in the UV behavior of the propagator and is probably connected to that in another UV property, namely renormalizability property of the two., Comment: 9 pages, 2 figures

We propose a new concept, the transversely trapping surface (TTS), as an extension of the static photon surface characterizing the strong gravity region of a static/stationary spacetime in terms of photon behavior. The TTS is defined as a static/stationary timelike surface $S$ whose spatial section is a closed two-surface, such that arbitrary photons emitted tangentially to $S$ from arbitrary points on $S$ propagate on or toward the inside of $S$. We study the properties of TTSs for static spacetimes and axisymmetric stationary spacetimes. In particular, the area $A_0$ of a TTS is proved to be bounded as $A_0\le 4\pi(3GM)^2$ under certain conditions, where $G$ is the Newton constant and $M$ is the total mass. The connection between the TTS and the loosely trapped surface proposed by us [arXiv:1701.00564] is also examined., Comment: 22 pages, 4 figures, title slightly modified, discussion and references added, published version

We discuss the uniqueness of the static spacetimes with non-trivial conformal scalar field. Then, we can show that the spacetime is unique to be the Bocharova-Bronnikov-Melnikov-Bekenstein solution outside the surface composed of the unstable circular orbit of photon(photon surface). In addition, we see that multi-photon surfaces having the same scalar field values do not exist., Comment: 6 pages, references added, introduction and discussion improved

For asymptotically flat spacetimes, using the inverse mean curvature flow, we show that any compact $2$-surface, $S_0$, whose mean curvature and its derivative for outward direction are positive in spacelike hypersurface with non-negative Ricci scalar satisfies the inequality $A_0 \leq 4 \pi (3Gm)^2$, where $A_0$ is the area of $S_0$ and $m$ is the total mass. The upper bound is realized when $S_0$ is the photon sphere in a hypersurface isometric to $t=$const. slice of the Schwarzschild spacetime., Comment: 5 pages, a reference added, minor changes, accepted for publication in PTEP

We discuss the uniqueness of the static black hole in the Einstein gravity with a conformally coupled scalar field. In particular, we prove the uniqueness of the region outside of the photon surface, not event horizon., Comment: 7 pages, some comments added, accepted for publication in PTEP

We obtain the effective theory for the non-linear dynamics of black branes---both neutral and charged, in asymptotically flat or Anti-deSitter spacetimes---to leading order in the inverse-dimensional expansion. We find that black branes evolve as viscous fluids, but when they settle down they are more naturally viewed as solutions of an elastic soap-bubble theory. The two views are complementary: the same variable is regarded in one case as the energy density of the fluid, in the other as the deformation of the elastic membrane. The large-D theory captures finite-wavelength phenomena beyond the conventional reach of hydrodynamics. For asymptotically flat charged black branes (either Reissner-Nordstrom or p-brane-charged black branes) it yields the non-linear evolution of the Gregory-Laflamme instability at large D and its endpoint at stable non-uniform black branes. For Reissner-Nordstrom AdS black branes we find that sound perturbations do not propagate (have purely imaginary frequency) when their wavelength is below a certain charge-dependent value. We also study the polarization of black branes induced by an external electric field., Comment: 26 pages. v2: 33 pages. Appendix added with a systematic derivation of the effective equations. v3: 34 pages. Expanded introduction

We study tree-unitarity and renormalizability in Lifshitz-scaling theory, which is characterized by an anisotropic scaling between the spacial and time directions. Due to the lack of the Lorentz symmetry, the conditions for both unitarity and renormalizability are modified from those in relativistic theories. For renormalizability, the conventional discussion of the power counting conditions has to be extended. Because of the dependence of $S$-matrix elements on the reference frame, unitarity requires stronger conditions than those in relativistic cases. We show that the conditions for unitarity and renormalizabilty are identical as in relativistic theories. We discuss the importance of symmetries for a theory to be renormalizable., Comment: 6pages. Proceedings for the 2nd LeCosPA Symposium: Everything about Gravity, Celebrating the Centenary of Einstein's General Relativity. Talk delivered by K. Izumi on December 17, 2015, Taipei, Taiwan

We study unitarity and renormalizability in the Lifshitz scalar field theory, which is characterized by an anisotropic scaling between the space and time directions. Without the Lorentz symmetry, both the unitarity and the renormalizability conditions are modified from those in relativistic theories. We show that for renormalizability, an extended version of the power counting condition is required in addition to the conventional one. The unitarity bound for S-matrix elements also gives stronger constraints on interaction terms because of the reference frame dependence of scattering amplitudes. We prove that both unitarity and renormalizability require identical conditions as in the case of conventional relativistic theories., Comment: 31 pages, 11 figures

We discuss the boundary effect of anomaly-induced action in two-dimensional spacetime, which is ignored in previous studies. Anomaly-induced action, which gives the stress tensor with the same trace as the trace anomaly, can be represented in terms of local operators by introducing an auxiliary scalar field. Although the degrees of freedom of the auxiliary field can in principle describe the quantum states of the original field, the principal relation between them was unclear. We show here that, by considering the boundary effect, the solutions of classical auxiliary fields are naturally related to the quantum states of the original field. We demonstrate this conclusion via several examples such as the flat, black hole and the de Sitter spacetime., Comment: 15 pages, 8 figures