Asymptotic Symmetries and Weinberg's Soft Photon Theorem in Minkd+2_{d+2}

We show that Weinberg's leading soft photon theorem in massless abelian gauge theories implies the existence of an infinite-dimensional large gauge symmetry which acts non-trivially on the null boundaries ${\mathscr I}^\pm$ of $(d+2)$-dimensional Minkowski spacetime. These symmetries are parameterized by an arbitrary function $\varepsilon(x)$ of the $d$-dimensional celestial sphere living at ${\mathscr I}^\pm$. This extends the previously established equivalence between Weinberg's leading soft theorem and asymptotic symmetries from four and higher even dimensions to \emph{all} higher dimensions.Comment: 30 pages; v2: Added reference and minor clarification comments, fixed minor typos, version to appear in JHE

Limitations on Dimensional Regularization in Renyi Entropy

Dimensional regularization is a common method used to regulate the UV divergence of field theoretic quantities. When it is used in the context of Renyi entropy, however, it is important to consider whether such a procedure eliminates the statistical interpretation thereof as a measure of entanglement of states living on a Hilbert space. We therefore examine the dimensionally regularized Renyi entropy of a 4d unitary CFT and show that it admits no underlying Hilbert space in the state-counting sense. This gives a concrete proof that dimensionally regularized Renyi entropy cannot always be obtained as a limit of the Renyi entropy of some finite-dimensional quantum system.Comment: 10 pages; v2: Minor corrections of typos; v3: Small modification of conclusion sectio

Entanglement Entropy in Lifshitz Theories

We discuss and compute entanglement entropy (EE) in (1+1)-dimensional free Lifshitz scalar field theories with arbitrary dynamical exponents. We consider both the subinterval and periodic sublattices in the discretized theory as subsystems. In both cases, we are able to analytically demonstrate that the EE grows linearly as a function of the dynamical exponent. Furthermore, for the subinterval case, we determine that as the dynamical exponent increases, there is a crossover from an area law to a volume law. Lastly, we deform Lifshitz field theories with certain relevant operators and show that the EE decreases from the ultraviolet to the infrared fixed point, giving evidence for a possible c-theorem for deformed Lifshitz theories.Comment: 24 pages, 8 figures; v2: Clarified discussions in Subsection 3.3 and appendix; v3: Major extension of results, including an analytic computation of subinterval entanglement in massless scalar Lifshitz theories; v4: Added footnote 4 for clarification, version to appear in SciPos

New Symmetries of Massless QED

An infinite number of physically nontrivial symmetries are found for abelian gauge theories with massless charged particles. They are generated by large $U(1)$ gauge transformations that asymptotically approach an arbitrary function $\varepsilon(z,\bar{z})$ on the conformal sphere at future null infinity ($\mathscr I^+$) but are independent of the retarded time. The value of $\varepsilon$ at past null infinity ($\mathscr I^-$) is determined from that on $\mathscr I^+$ by the condition that it take the same value at either end of any light ray crossing Minkowski space. The $\varepsilon\neq$ constant symmetries are spontaneously broken in the usual vacuum. The associated Goldstone modes are zero-momentum photons and comprise a $U(1)$ boson living on the conformal sphere. The Ward identity associated with this asymptotic symmetry is shown to be the abelian soft photon theorem.Comment: 17 pages, v2: typos in equations correcte

On Entropy Growth in Perturbative Scattering

Inspired by the second law of thermodynamics, we study the change in subsystem entropy generated by dynamical unitary evolution of a product state in a bipartite system. Working at leading order in perturbative interactions, we prove that the quantum $n$-Tsallis entropy of a subsystem never decreases, $\Delta S_n \geq 0$, provided that subsystem is initialized as a statistical mixture of states of equal probability. This is true for any choice of interactions and any initialization of the complementary subsystem. When this condition on the initial state is violated, it is always possible to explicitly construct a ``Maxwell's demon'' process that decreases the subsystem entropy, $\Delta S_n < 0$. Remarkably, for the case of particle scattering, the circuit diagrams corresponding to $n$-Tsallis entropy are the same as the on-shell diagrams that have appeared in the modern scattering amplitudes program, and $\Delta S_n \geq 0$ is intimately related to the nonnegativity of cross-sections.Comment: 6 page

Marginal independence and an approximation to strong subadditivity

Given a multipartite quantum system, what are the possible ways to impose mutual independence among some of the parties, and the presence of correlations among others, such that there exists a quantum state which satisfies these demands? This question and the related notion of a \textit{pattern of marginal independence} (PMI) were introduced in arXiv:1912.01041, and then argued in arXiv:2204.00075 to distill the essential information for the derivation of the holographic entropy cone. Here we continue the general analysis initiated in arXiv:1912.01041, focusing in particular on the implications of the necessary condition for the saturation of subadditivity. This condition, which we dub Klein's condition, will be interpreted as an approximation to strong subadditivity for PMIs. We show that for an arbitrary number of parties, the set of PMIs compatible with this condition forms a lattice, and we investigate several of its structural properties. In the discussion we highlight the role played by the \textit{meet-irreducible elements} in the solution of the quantum marginal independence problem, and by the \textit{coatoms} in the holographic context. To make the presentation self-contained, we review the key ingredients from lattice theory as needed.Comment: 62 pages, 10 figure

Covariant phase space and soft factorization in non-Abelian gauge theories

Abstract: We perform a careful study of the infrared sector of massless non-abelian gauge theories in four-dimensional Minkowski spacetime using the covariant phase space formalism, taking into account the boundary contributions arising from the gauge sector of the theory. Upon quantization, we show that the boundary contributions lead to an infinite degeneracy of the vacua. The Hilbert space of the vacuum sector is not only shown to be remarkably simple, but also universal. We derive a Ward identity that relates the n-point amplitude between two generic in- and out-vacuum states to the one computed in standard QFT. In addition, we demonstrate that the familiar single soft gluon theorem and multiple consecutive soft gluon theorem are consequences of the Ward identity