Quantum Fields and Strings

Motivated by the problem of defining the entanglement entropy of the graviton, we study the division of the phase space of general relativity across subregions. Our key requirement is demanding that the separation into subregions is imaginary---i.e., that entangling surfaces are not physical. This translates into a certain condition on the symplectic form. We find that gravitational subregions that satisfy this condition are bounded by surfaces of extremal area. We characterise the 'centre variables' of the phase space of the graviton in such subsystems, which can be taken to be the conformal class of the induced metric in the boundary, subject to a constraint involving the traceless part of the extrinsic curvature. We argue that this condition works to discard local deformations of the boundary surface to infinitesimally nearby extremal surfaces, that are otherwise available for generic codimension-2 extremal surfaces of dimension ≥ 2.

I will discuss how holographic and effective field theory methods could shed light on important open questions in low energy condensed matter systems. I will focus on the study of the vibrational degrees of freedom, i.e. ''phonons'', in liquids, solids and disordered systems like glasses. Building intuition from the holographic systems I will tackle the problem of the low frequency elastic response in liquids and the universal emergence of the boson peak in ordered crystals and amorphous solids.

Part 1 is about anomalies and how they can deform generalized global symmetry into 2-group global symmetry.  This is illustrated with simple QFT examples in 4d.  Part 2 is about 6d.

6d theories with 2-group symmetry exist, but cannot be conformal.  6d superconformal theories (SCFTs) cannot have 2-group or higher-form, generalized global symmetries.  This requires cancellation of mixed gauge and global terms in the anomaly polynomial.   SCFT relations between conformal and ’t Hooft anomalies will also be discussed.   Based on papers with Cordova and Dumitrescu.

Bulk coherent states produced by Euclidean CFT sources can be used to study how geometry arises from entanglement: when these states obey the Ryu-Takayanagi formula, the linearized Einstein equations hold in the bulk without assuming the complete AdS/CFT correspondence.  However, the Faulkner-Lewkowycz-Maldacena bulk entanglement term that corrects the RT formula does not play a role in these previous studies, since to leading order coherent states have the same entanglement entropy as the vacuum.  We study states CFT states created by Euclidean, bilocal, double trace sources, which produce bulk squeezed states.  We consider possible modifications to RT and study divergences in the perturbative expansion that occur for certain choices of source.  We work towards determining constraints on the bulk geometry and state that arise from requiring FLM, akin to the linearized Einstein equations that arose for coherent states.

We review the color memory effect which is the non-abelian gauge theory analog of the gravitational memory effect, in which the passage of color radiation induces a net relative SU(3) color rotation of a pair of nearby quarks. Then, we show how the color memory effect arises in Regge limit scattering processes and propose that this effect can be measured in the Regge limit of deeply inelastic scattering at electron-ion colliders.

In this talk I will consider the S-matrix bootstrap of four dimensional scattering amplitudes with O(3) symmetry and no bound states and apply the formalism to pion physics. I will discuss the remarkable location where QCD seems to lie in the multi-dimensional space of zeros, scattering length and resonance mass values, based on various experimental and theoretical expectations.

We consider implications of superrotations as an asymptotic symmetry of asymptotically flat spacetimes.  Beginning with a review of the rich structure of interconnections between soft theorems, asymptotic symmetries, and                 memory effects, we describe the superrotation iteration.  The subleading soft graviton theorem can be cast as a Ward identity for this asymptotic symmetry in 4D, and also as one for the stress tensor of a putative CFT2.  We detail the change of scattering basis motivated by this asymptotic symmetry and discuss recent progress.

In gauge theories, there is an inherent tension between locality and gauge invariance.   This is precisely expressed by the failure to factorize the physical Hilbert space into local tensor products.   The extended Hilbert space offers a resolution to this problem by embedding physical states into a larger Hilbert space containing gauge variant degrees of freedom.  For two dimensional TQFT's, we show how this extension fits inside the framework of extended quantum field theory, as described by the Moore-Segal axioms.  These are sewing axioms that impose a sort of spacetime covariance for the extended Hilbert space.   For the case of two-dimensional Yang Mills and it's string theory dual, we show how this framework leads to exact calculations of multi-interval modular flow,  ,negativity, and entanglement entropy.  Moreover, we given an axiomatic formulation of the "entanglement brane", which nicely compliments the worldsheet description given in previous work.

The two-point functions <O^n(x) Obar^n(y)> for generator O of Coulomb branch chiral rings in D=4 N=2 SCFT will be determined universally to all orders in 1/n by the theory's a-anomaly.
The calculation will be done using the method of large-charge expansion presented in [1706.05743]; the absence of F-terms in the (R-charge)^(-1) expansion of the effective action ensures this universality.
I will also comment on the non-universal and non-perturbative corrections to the two-point functions whose leading piece was numerically shown to go as O(exp(-sqrt(n))).  

In this talk I will review the results of recent work in collaboration with  Cecilia De Fazio, Benjamin Doyon and István M. Szécsényi. We studied the entanglement of excited states consisting of a finite number of particle excitations. More precisely, we studied the difference between the entanglement entropy of such states and that of the ground state in a simple bi-partition of a quantum system, where both the size of the system and of the bi-partition are infinite, but their ratio is finite. We originally studied this problem in massive 1+1 dimensional QFTs where analytic computations were possible. We have found the results to apply more widely, including to higher dimensional free theories. In all cases we find that the increment of entanglement is a simple function of the ratio between region's and system's size only. Such function, turns out to be exactly the entanglement of a qubit state where the coefficients of the state are simply associated with the probabilities of particles being localised in one or the other part of the bi-partition. In this talk I will describe the results in some detail and discuss their domain of applicability. I will also highlight the main QFT techniques that we have used in order to obtain them analytically and  present some numerical data. 

In the context of the AdS(4)/BCFT(3) correspondence, we study the holographic entanglement entropy for spatial regions having arbitrary shape. An analytic expression for the subleading term with respect to the area law is discussed. When the bulk spacetime is a part of AdS(4),
this formula becomes the Willmore functional with a proper boundary term evaluated on the minimal surface viewed as a submanifold of the three dimensional flat Euclidean space with a boundary. 
Numerical checks of this formula are performed through a code which allows to construct minimal area surfaces anchored to generic curves. For some simple regions like infinite strips and disks, analytic results are obtained and they confirm the general expression for the subleading term. In particular, when the spatial region contains corners adjacent to the boundary, a logarithmic divergence occurs whose coefficient is determined by a so-called corner function which depends on the boundary conditions. An analytic expression for the holographic corner function and its checks are also discussed.