Quantum Fields and Strings

The study of string scattering in general curved spacetimes presents a stark contrast to the relatively well-understood framework in flat space, where perturbative techniques and worldsheet methods can be used. However, the AdS/CFT correspondence offers a powerful indirect method to compute string amplitudes in AdS. In this talk, I will present recent developments in the AdS Virasoro-Shapiro program. The tree-level amplitude of four gravitons in AdS^5 x S^5 is mapped to a four-point correlator in N=4 SYM at large central charge, and studied by CFT methods combined with single-valuedness, which echoes its importance in flat space. The amplitude itself is defined and constructed as an expansion around flat space. While the goal is to compute it to all orders, attention can be placed on more tractable limits. I will present our results for the High Energy limit, with dual insights from the spacetime and worldsheet perspectives, and the richer case of the Regge limit, which encodes full information on the intermediate operators in the leading Regge trajectory.

We construct the phase space of a spherically symmetric causal diamond in (d+2)-dimensional Minkowski spacetime. Utilizing the covariant phase space formalism, we identify the relevant degrees of freedom that localize to the d-dimensional bifurcate horizon and, upon canonical quantization, determine their commutators. On this phase space, we find two Iyer-Wald charges. The first of these charges, proportional to the area of the causal diamond, is responsible for shifting the null time along the horizon and has been well-documented in the literature. The second charge is much less understood, being integrable for d ≥ 2 only if we allow for field-dependent diffeomorphisms and is responsible for changing the size of the causal diamond. 

"Null Polygons" in N=4 SYM theory describe the multi-point correlators of 1/2-BPS local operators with large R-charge, when they approach the vertices of a light-like polygon. The leading UV divergences of null polygons is conjectured to satisfy a hierarchy of coupled Toda field theory equations [E.O., Vieira ’22]. I will present some progress towards the prediction of Null Polygons beyond leading logarithms via the hexagons technique, appropriately truncated in the light-cone regime. The method, still conjectural, relies on a series of weak-coupling derivations performed in the Fishnet limit of the theory, where the hexagon representation is derived in the basis of eigenfunctions of a conformal Heisenberg magnet in the principal series. I will present a number of worked-out examples for multi-point multi-loop Fishnet Feynman integrals and Null Polygons.

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In this talk I will describe the correspondence between the double scaling limit of the SYK model and infinite temperature and de Sitter gravity in 2 and 3 dimensions. The dictionary involves a precise match between the chord rules that govern the SYK correlation functions and the braid interactions between line operators in the gravity theory.

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Topological strings are well understood in perturbation theory, but their non-perturbative structure has been the subject of much work and speculation. A useful approach to this problem is to unveil the non-perturbative sectors of the theory by looking at the large order behavior of the perturbative series. This approach can be formulated in a mathematically rigorous way by using the theory of resurgence. In this talk I review the basic ideas behind this approach and I show that it can be successfully applied to topological string theory on arbitrary Calabi-Yau threefolds. Thsee methods lead, not only to explicit non-perturbative topological string amplitudes, but also to a conjecture relating the “invariants” of the theory of resurgence (also known as Stokes constants) to BPS invariants. Physically, this conjecture implies that the large order behavior of the topological string perturbative series contains information about the spectrum of stable D-brane sectors.

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Moduli spaces of vacua are an intriguing property of certain supersymmetric QFTs which have been widely explored. However, a first-principles approach to moduli spaces and how they constrain observables is still lacking. This question is even more pressing due to recent interest in moduli spaces in theories with only two supercharges, where supersymmetry is extremely weak and does not allow for exact computations. In this talk we attempt to bootstrap conformal field theories with moduli spaces. First we assume an additional global symmetry which is spontaneously broken along the moduli space, and use techniques from the large charge expansion to show that the existence of a moduli space directly constrains CFT data of charged operators. We then study the generic case by using a "moduli space bootstrap equation" to write down perturbative sum rules on observables of CFTs order-by-order in a small coupling. We discuss several examples and applications of our results. 

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Determining the long-range phase of matter of a strongly coupled system from its microscopic description has long been one of the central topics in physics. Simple microscopic systems often become strongly coupled at long range where we usually rely on clever approximations. Bootstrap is an alternative approach that uses positivity and equations of motion to make predictions in quantum many-body systems without making approximations. In this talk, I will show my recent work on using bootstrap to compute the ground state energy, local observables and gaps of a quantum many-body system in the thermodynamic limit with rigorous error bars.

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Holographic conformal field theories exhibit dramatic changes in the structure of their operator algebras in the limit where the number of local degrees of freedom (N) becomes infinite. An important example of such phenomena is the violation of the additivity property for algebras associated to local subregions. We investigate the consequences of this "additivity anomaly" in the context of holographic duality. We propose that the difference in volumes of bulk dual subregions can be used as a holographic measure for this additivity anomaly of large N boundary algebras. We demonstrate how the additivity anomaly underlies the success of quantum error correcting code models of holography. Finally, we argue that the connected wedge theorems (CWTs) of May, Penington, Sorce, and Yoshida can be re-phrased in terms of the additivity anomaly, allowing for the definition of a generalized scattering region for which a generalization of the CWTs can be formulated such that both the theorem and its converse should hold.

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I will talk about the boundary vertex operator algebra of topologically twisted 3d N=4 rank-zero SCFTs. The latter is recently introduced family of N=4 SCFTs with zero-dimensional Higgs and Coulomb branches, which are expected to support rational VOAs at the boundary. I will discuss the construction of the simplest class of rank-zero SCFTs T_r, and argue that they admit the simple affine VOAs L_r(osp(1|2)) at their boundary. In the simplest case, this leads to a physical realization of a novel level-rank duality between L_1(osp(1|2)) and the Virasoro minimal model M(2,5).

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Several years ago, Nayak and Else argued that Symmetry Protected Topological phases in d dimensions can be classified using non-on-site actions of the symmetry group in d-1 dimensions. Such non-on-site actions can have an “anomaly”, in the sense that the symmetry action cannot be consistently localized. This anomaly is similar but distinct from ’t Hooft anomaly in QFT. Nayak and Else assumed that the symmetry group is finite and the non-on-site action is given by a finite-depth local unitary circuit. I will explain how to generalize the construction of the anomaly index in two directions: to Lie groups as well as to arbitrary actions which preserve locality. For simplicity, I will only discuss the one-dimensional case. One can prove that a nonzero anomaly index prohibits any invariant 1d Hamiltonian from having invariant ground states. This is similar to ’t Hooft anomaly matching in QFT. Lieb-Schultz-Mattis-type theorems arise as a special case where the symmetry group involves translations. This is joint work with Nikita Sopenko.

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Zoom link https://pitp.zoom.us/j/95661517248?pwd=SkMxUFJWTG56SG9hVlNiNS9yeEVrQT09