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The full theory of Quantum Gravity (QG) that unites gravity and quantum mechanics has not yet been discovered. One of the pressing issues is to correctly account for unitarity in quantum mechanical processes, even on a static curved spacetime. The presence of black holes in particular leads to profound issues with unitary evolution and locality. Though Hawking radiation and gravitational interactions are well studied in the Heisenberg picture, this work uses the Schr\"{o}dinger picture to examine their evolution. Through the ADM decomposition and the associated Hamiltonian we can study the Schr\"{o}dinger picture, and define the unitary time evolution operator, as in regular quantum mechanics. By carefully examining the Schr\"{o}dinger picture, we aim to provide a clearer understanding of QG, and defer the study of changes needed to unitarize the theory to later work. This thesis focuses in particular on massless scalar fields propagating on curved spacetimes of dimension $D\geq 4$. The simplicity of the scalar field is a useful test case, and we expect to be able to generalize to other, more complicated fields. First, Hawking radiation is studied for Schwarzschild black holes in the Schr\"{o}dinger picture. Using the ADM decomposition, ``nice slices'' are introduced, which are smooth foliations of the spacetime that are regular across the horizon, rather than the more typical singular ones involving tortoise coordinates. The role of ultra high energy Hawking modes is discussed, and these are found to be a result of the choice of singular coordinates used near the horizon, rather than an indication of transplanckian physics occurring on the horizon scale. In addition, the constraint equations, which are the ADM decomposition of the Einstein equations, are expanded to second order in $\kappa = \sqrt{32 \pi G}$ in an arbitrary background spacetime. Observable operators are ``dressed'' in their gravitational fields, in analogy with the description from quantum field theories, and the creation of such an operator makes an associated field which extends to infinity. A general form for the gravitational dressing is found to leading order using the expansion of the constraint equations.

The Dunkl--Dirac operator is a deformation of the Dirac operator by means of Dunkl derivatives. We investigate the symmetry algebra generated by the elements supercommuting with the Dunkl--Dirac operator and its dual symbol. This symmetry algebra is realised inside the tensor product of a Clifford algebra and a rational Cherednik algebra associated with a reflection group or root system. For reducible root systems of rank three, we determine all the irreducible finite-dimensional representations and conditions for unitarity. Polynomial solutions of the Dunkl--Dirac equation are given as a realisation of one family of such irreducible unitary representations., Comment: v3 40p. Final version accepted in J. Algebra. See v2 for proof of Thm 4.1

We build a quantum cellular automaton (QCA) which coincides with 1 + 1 QED on its known continuum limits. It consists in a circuit of unitary gates driving the evolution of particles on a one dimensional lattice, and having them interact with the gauge field on the links. The particles are massive fermions, and the evolution is exactly U(1) gauge-invariant. We show that, in the continuous-time discrete-space limit, the QCA converges to the Kogut-Susskind staggered version of 1 + 1 QED. We also show that, in the continuous spacetime limit and in the free one particle sector, it converges to the Dirac equation—a strong indication that the model remains accurate in the relativistic regime.

The uncertainty principle is one of the fundamental features of quantum mechanics and plays a vital role in quantum information processing. We study uncertainty relations based on metric-adjusted skew information for finite quantum observables. Motivated by the paper [Physical Review A 104, 052414 (2021)], we establish tighter uncertainty relations in terms of different norm inequalities. Naturally, we generalize the method to uncertainty relations of metric-adjusted skew information for quantum channels and unitary operators. As both the Wigner-Yanase-Dyson skew information and the quantum Fisher information are the special cases of the metric-adjusted skew information corresponding to different Morozova-Chentsov functions, our results generalize some existing uncertainty relations. Detailed examples are given to illustrate the advantages of our methods., Comment: 14 pages, 3 figures

Physical review letters 130(7), 071602 (2023). doi:10.1103/PhysRevLett.130.071602, We study coupled unitary Virasoro minimal models in the large rank (m→∞) limit. In large m perturbation theory, we find two nontrivial IR fixed points which exhibit irrational coefficients in several anomalous dimensions and the central charge. For N>4 copies, we show that the IR theory breaks all possible currents that would otherwise enhance the Virasoro algebra, up to spin 10. This provides strong evidence that the IR fixed points are examples of compact, unitary, irrational conformal field theories with the minimal amount of chiral symmetry. We also analyze anomalous dimension matrices for a family of degenerate operators with increasing spin. These display further evidence of irrationality and begin to reveal the form of the leading quantum Regge trajectory., Published by APS, College Park, Md.

We compute the $2\rightarrow 2$ gravitino scattering amplitudes at tree level in supergravity theories where supersymmetry is spontaneously broken. In the unitary gauge, the gravitino becomes massive (of mass $m_{3/2}$) by absorbing the Goldstino, and the scattering amplitudes of its longitudinal polarisations grow with energy as $\kappa^2 E^4/m_{3/2}^2$, signaling a potential breakdown of unitarity at a scale $\Lambda^2\sim m_{3/2}/\kappa\sim M_{\mathrm{SUSY}}^2$. As we show explicitly in the Polonyi model, this leading term is cancelled by the contributions coming from the scalar partner of the Goldstino (sgoldstino), restoring perturbative unitarity up to the Planck scale. This is expected since supersymmetry is spontaneously broken, in analogy with the situation occuring in the Standard Model, where massive gauge bosons scattering preserves unitarity at high energy once we consider the contributions from the Higgs boson. However, when supersymmetry is broken by the new Fayet-Iliopoulos $D$-term, with ungauged R-symmetry, the above cancellation does not occur. In this case, the unbroken phase is singular and there is no contribution able to cancel the quartic divergences of the amplitudes, leading to a cutoff $\Lambda\sim M_\mathrm{SUSY}$ where the effective theory breaks down. The same behaviour is obtained when supersymmetry is non-linearly realised., Comment: 22 pages, 1 figure

The non-forward eikonal scattering matrix for dipole-proton scattering at high energy obtains an imaginary part due to a $C$-odd three gluon exchange. We present numerical estimates for the perturbative Odderon amplitude as a function of dipole size, impact parameter, their relative azimuthal angle, and light-cone momentum cutoff $x$. The proton is approximated as $\psi_\mathrm{qqq}|qqq\rangle + \psi_\mathrm{qqqg}|qqqg\rangle$, where $\psi_\mathrm{qqq}$ is a non-perturbative three quark model wave function while the gluon emission is computed in light-cone perturbation theory. We find that the Odderon amplitude increases as $x$ decreases from 0.1 to 0.01. At yet lower $x$, the reversal of this energy dependence would reflect the onset of universal small-$x$ renormalization group evolution., Comment: 6 pages, 5 figures. Odderon amplitudes at different momentum fraction x included in the ancillary files

We continue to investigate correspondences between, on the one hand, scattering amplitudes for massive higher-spin particles and gravitons in appropriate quantum-to-classical limits, and on the other hand, classical gravitational interactions of spinning black holes according to general relativity. We first construct an ansatz for a gravitational Compton amplitude, at tree level, constrained only by locality, crossing symmetry, unitarity and consistency with the linearized-Kerr 3-point amplitude, to all orders in the black hole's spin. We then explore the extent to which a unique classical Compton amplitude can be identified by comparing with the results of the classical process of scattering long-wavelength gravitational waves off an exact Kerr black hole, determined by appropriate solutions of the Teukolsky equation. Up to fourth order in spin, we find complete agreement with a previously conjectured exponential form of the tree-level Compton amplitude. At higher orders, we extract tree-level contributions from the Teukolsky amplitude by an analytic continuation from a physical ($a/GM1$) regime. Up to the sixth order in spin, we identify a unique \textit{conservative} part of the amplitude which is insensitive both to the choice of boundary conditions at the black hole horizon and to branch choices in the analytic continuation. The remainder of the amplitude is determined modulo an overall sign from a branch choice, with the sign flipping under exchanging purely ingoing and purely outgoing boundary conditions at the horizon. Along the way, we make contact with novel applications of massive spinor-helicity variables pertaining to their relation to EFT operators and (spinning) partial amplitudes., v3: References added, Journal version. An incorrect derivation of the aligned spin scattering angle presented in section 5 in v2, was removed from v3 of this paper

We consider the physical implications of very light axiodilatons motivated by a novel mechanism to substantially reduce the vacuum energy proposed in arXiv:2110.10352. We address the two main problems concerning the light axiodilaton that appears in the low-energy limit, namely that the axion has a very low decay constant $f_a \sim $ eV (as read from its kinetic term) and that the dilaton is subject to bounds that are relevant to tests of GR once $\rho_{\rm vac} \leq 10^{-80} M_p^4$. We show that eV scale axion decay constants need not be a problem by showing how supersymmetric extra dimensions provide a sample unitarization for axion physics above eV scales for which non-anomalous matter/axiodilaton couplings can really have gravitational strength, showing how naive EFT reasoning can mistakenly overestimates axion interactions at eV. When axions really do couple strongly at eV scales we identify the dimensionless interaction in the UV completion that is also O(1), and how axion energy-loss bounds map onto known extra-dimensional constraints. We find a broad new class of exact exterior solutions to the vacuum axiodilaton equations and knowledge of axiodilaton-matter couplings also allows us to numerically search for interior solutions that match to known exterior solutions that can evade solar-system tests. We find no examples that do so, but also identify potential new candidate mechanisms for reducing the effective dilaton-matter coupling to gravitating objects without also undermining the underlying suppression of $\rho_{\rm vac}$., Comment: 28 pages, 11 figures. Minor comment added

We study quantum circuits consisting of unitary gates, projective measurements, and control operations that steer the system towards a pure absorbing state. Two types of phase transition occur as the rate of these control operations is increased: a measurement-induced entanglement transition, and a directed percolation transition into the absorbing state (taken here to be a product state). In this work we show analytically that these transitions are generically distinct, with the quantum trajectories becoming disentangled before the absorbing state transition is reached, and we analyze their critical properties. We introduce a simple class of models where the measurements in each quantum trajectory define an Effective Tensor Network (ETN) -- a subgraph of the initial spacetime graph where nontrivial time evolution takes place. By analyzing the entanglement properties of the ETN, we show that the entanglement and absorbing-state transitions coincide only in the limit of infinite local Hilbert-space dimension. Focusing on a Clifford model which allows numerical simulations for large system sizes, we verify our predictions and study the finite-size crossover between the two transitions at large local Hilbert space dimension. We give evidence that the entanglement transition is governed by the same fixed point as in hybrid circuits without feedback., 18 pages, 9 figures; v2: Appendix added, minor revision

39th International Symposium on Lattice Field Theory, Lattice 2022, Bonn, Germany, 8 Aug 2022 - 13 Aug 2022; Proceedings of Science / International School for Advanced Studies (LATTICE2022), 357 (2023). doi:10.22323/1.430.0357, We present preliminary results for a scale setting procedure based on a mixed action strategy consisting of Wilson twisted mass valence fermions at maximal twist on CLS ensembles with $N_f=2+1$ flavours of O($a$)-improved Wilson sea quarks. Once the matching of valence and sea quark masses is performed, universality tests are carried out by comparing the continuum-limit results of the mixed action setup to those of the regularisation based solely on O($a$)-improved Wilson fermions. The scale setting uses the pion and kaon decay constants, in units of the gradient flow scale $t_0$, obtained from combining computations with the unitary Wilson action and the mixed action. The proper isolation of ground states as well as the continuum-chiral extrapolations are evaluated through model variation techniques. An update on the determination of $t_0$ will be presented., Published by SISSA, Trieste

Formulating a relativistic equation for particles with arbitrary spin remains an open challenge in theoretical physics. In this study, the main algebraic approaches used to generalize the Dirac and Kemmer Duffin equations for particles of arbitrary spin are investigated. It is proved that an irreducible relativistic equation formulated using spin matrices satisfying the commutation relations of the anti-de Sitter group leads to inconsistent results, mainly as a consequence of violation of unitarity and the appearance of a mass spectrum that does not reflect the physical reality of elementary particles. However, the introduction of subsidiary conditions resolves the problem of unitarity and restores the physical meaning of the mass spectrum. The equations obtained by these approaches are solved and the physical nature of the solutions is discussed., 26 pages, 1 figure

We present the Standard Model Effective Field Theories (SMEFT) from purely on-shell arguments. Starting from a few basic assumptions such as Poincar\'e invariance and locality, we classify all the renormalisable and non-renormalisable interactions at the lowest order in the couplings. From these building blocks, we review how locality and unitarity enforce Lie algebra structures to appear in the S-matrix elements together with relations among couplings (and hypercharges). Furthermore, we give a fully on-shell algorithm to compute any higher-point tree-level amplitude (or form factor) in generic EFTs, bypassing BCFW-like recursion relations which are known to be problematic when non-renormalisable interactions are involved. Finally, using known amplitudes techniques we compute the mixing matrix of SMEFT irrelevant interactions up to mass dimension 8, to linear order in the effective interactions., Comment: 39 + 14 pages; v3:matched published version, typos corrected

Hasse diagrams (or phase diagrams) for moduli spaces of supersymmetric field theories have been intensively studied in recent years, and many tools to compute them have been developed. The moduli space of instantons, despite being well studied, has proven difficult to deal with. In this note we explore the Hasse diagram of this moduli space from several perspectives — using the partial Higgs mechanism, using brane systems and using quiver subtraction — having to refine previously developed techniques. In particular we introduce the new concept of decorated quiver, which allows to deal with a large class of unitary quivers, including those with adjoint matter.

We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the $n^{\text{th}}$ R\'enyi entropy includes a wormhole between the $n$ copies of the gravitating universe, leading to a standard "island formula" for entanglement entropy consistent with unitarity of quantum information. When both universes contain gravity, gravitational corrections to this configuration lead to a violation of unitarity. However, the path integral is now dominated by a novel wormhole with $2n$ boundaries connecting replica copies of both universes. The analytic continuation of this contribution involves a quotient by $\mathbb{Z}_n$ replica symmetry, giving a cylinder connecting the two universes. When entanglement is large, this configuration has an effective description as a "swap wormhole", a geometry in which the boundaries of the two universes are glued together by a "swaperator". This description allows precise computation of a generalized entropy-like formula for entanglement entropy. The quantum extremal surface computing the entropy lives on the Lorentzian continuation of the cylinder/swap wormhole, which has a connected Cauchy slice stretching between the universes -- a realization of the ER=EPR idea. The new wormhole restores unitarity of quantum information., Comment: 39 pages, 11 figures

A novel alternative to Einstein's general theory of relativity is presented, based on the gauge principle. The gravitational Lagrangian has no Einstein--Hilbert term, but is constructed from quadratic invariants of the Riemann--Cartan curvature and torsion, constituting a geometric gauge theory of the Poincaré group. Despite the introduction of Planck and cosmological constant scales through the torsion couplings, the linearised free theory is not only unitary but also power-counting renormalisable. A conformal symmetry in this regime is broken naturally in the nonlinear cosmology, for which constant axial torsion is an attractor state of the background. The Hubble dynamics are then identical to those of Friedmann up to a complete screening of the spatial curvature, and a boundary condition which can dynamically replicate the effects of dark radiation in the early Universe. In a simplified version of the theory, part of the torsion is removed via multipliers without detriment to the known phenomenology. This procedure introduces classical ghosts to the Minkowski background, but produces the Newtonian limit on the axial vector background anticipated in Nature.