arXiv subjects

Arvin Shahbazi-Moghaddam

Publications and source records attributed to Arvin Shahbazi-Moghaddam.

21 records · Page 2Linked to original sources

arXiv2019

Entropy Variations and Light Ray Operators from Replica Defects

We study the defect operator product expansion (OPE) of displacement operators in free and interacting conformal field theories using replica methods. We show that as $n$ approaches $1$ a contact term can emerge when the OPE contains defect operators of twist $d-2$. For interacting theories and general states we give evidence that the only possibility is from the defect operator that becomes the stress tensor in the $n\to 1$ limit. This implies that the quantum null energy condition (QNEC) is always saturated for CFTs with a twist gap. As a check, we show independently that in a large class of near vacuum states, the second variation of the entanglement entropy is given by a simple correlation function of averaged null energy operators as studied by Hofman and Maldacena. This suggests that sub-leading terms in the the defect OPE are controlled by a defect version of the spin-3 non-local light ray operator and we speculate about the possible origin of such a defect operator. For free theories this contribution condenses to a contact term that leads to violations of QNEC saturation.

hep-th↗

arXiv2018

Higher-Point Positivity

We consider the extension of techniques for bounding higher-dimension operators in quantum effective field theories to higher-point operators. Working in the context of theories polynomial in $X=(\partial ϕ)^2$, we examine how the techniques of bounding such operators based on causality, analyticity of scattering amplitudes, and unitarity of the spectral representation are all modified for operators beyond $(\partial ϕ)^4$. Under weak-coupling assumptions that we clarify, we show using all three methods that in theories in which the coefficient $λ_n$ of the $X^n$ term for some $n$ is larger than the other terms in units of the cutoff, $λ_n$ must be positive (respectively, negative) for $n$ even (odd), in mostly-plus metric signature. Along the way, we present a first-principles derivation of the propagator numerator for all massive higher-spin bosons in arbitrary dimension. We remark on subtleties and challenges of bounding $P(X)$ theories in greater generality. Finally, we examine the connections among energy conditions, causality, stability, and the involution condition on the Legendre transform relating the Lagrangian and Hamiltonian.

hep-th↗

arXiv2018

Energy is Entanglement

We compute the local second variation of the von Neumann entropy of a region in theories with a gravity dual. For null variations our formula says that the diagonal part of the Quantum Null Energy Condition is saturated in every state, thus providing an equivalence between energy and entropy. We prove that the formula holds at leading order in 1/N, and further argue that it will not be affected at higher orders. We conjecture that the QNEC is saturated in all interacting theories. We also discuss the special case of free theories, and the implications of our formula for the Averaged Null Energy Condition, Quantum Focusing Conjecture, and gravitational equations of motion. We show that the leading-order gravitational equations of motion, Einstein's equations, are equivalent to leading-order saturation of the QFC for Planck-width deformations.

hep-th↗