Quantum Fields and Strings

Motivated by recent interesting holographic results, several attempts have been made to study complexity ( rather " Circuit Complexity") for quantum field theories using Nielsen's geometric method. But most of the studies so far have been limited to free quantum field theory. In this talk we will take a baby step towards understanding the circuit  complexity for interacting quantum field theories. We will consider \lambda \phi^4 theory and discuss in detail how to set up the computation perturbatively in coupling. Our method enables us to study circuit complexity in the epsilon expansion for the Wilson-Fisher fixed point. We find that with increasing dimensionality the circuit depth increases in the presence of the \phi^4 interaction eventually causing the perturbative calculation to breakdown. We discuss how circuit complexity relates with the renormalization group. Finally we discuss several possible generalization and compare our results with other approaches.

Using knowledge about the spectrum of operators in N=4 SYM, consistency of OPE, and analytic bootstrap techniques, I will obtain 1- loop corrections for 4-pt functions of single particle half-BPS operators of IIB supergravity on AdS_5\timesS^5. Along the way, I will discuss a general formula for the leading anomalous dimension of all double-trace operators in the supergravity regime.

Recently I pointed out that reconstruction of interior operators can be interpreted as the Hayden-Preskill recovery. Building on this observation, I will propose a resolution of the firewall puzzle by describing a state-independent reconstruction of interior operators which does not lead to the non-local signaling. 

We show how the extended thermodynamics of hyperbolic black holes in AdS describes features of quantum information measures in quantum field theory, and discuss prospects for making further connections. In particular, the second law of thermodynamics is seen in this context to map to the generalized Zamolodchikov c-theorem, connecting these two firmly for the first time. Some projects for getting further lessons and perhaps new tools from  these connections (perhaps using holographic heat engines) are outlined. 

While the simplest Feynman diagrams evaluate to multiple polylogarithms, more complicated functions can arise, involving integrals over higher-dimensional manifolds. Surprisingly, all examples of such manifolds in the literature to date are Calabi-Yau. I discuss why this is, and prove that a specific class of "marginal" diagrams give rise to Calabi-Yau manifolds. I demonstrate a bound on the dimensionality of these manifolds with loop order, and present infinite families of diagrams that saturate this bound to all orders.

I will review recent and ongoing developments in path integral optimization and path integral complexity in 2d CFTs. After, I will discuss the connection with geometric approach to circuit complexity and point out several open problems.

Anomaly cancellation conditions place strong constraints on many physical theories. In the traditional framework, local and global anomalies are detected by computing an eta invariant of a certain Dirac operator on a mapping torus. Recent research has uncovered the existence of finer anomaly cancellation conditions, not visible in these traditional settings. I will review the traditional and refined anomalies, and apply them to various symmetries of interest in particle physics. Examples include the (various global forms of) the Standard Model, GUT's, and discrete gauge symmetries of physical interest such as proton triality and a certain Z4 symmetry in the (MS)SM.

In many-body chaotic systems, the size of an operator generically grows in Heisenberg evolution, which can be measured by certain out-of-time-ordered four-point functions. However, these only provide a coarse probe of the full underlying operator growth structure. We develop a methodology to derive the full growth structure of fermionic systems, that also naturally introduces the effect of finite temperature. We then apply our methodology to the SYK model, which features all-to-all q-body interactions. We derive the full operator growth structure in the large q limit at all temperatures. We see that its temperature dependence has a remarkably simple form consistent with the slowing down of scrambling as temperature is decreased. Furthermore, our finite-temperature scrambling results can be modeled by a modified epidemic model, where the thermal state serves as a vaccinated population, thereby slowing the overall rate of infection.

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.