Quantum Fields and Strings

The Kawai–Lewellen–Tye (KLT) relations are a striking example of how string theory can reveal hidden structures and connect a web of, in principle, very different theories. Originally, they state that (tree-level) closed-string amplitudes can be expressed as quadratic combinations of open-string amplitudes. In the field theory limit, this gives rise to the celebrated double-copy between gluons and gravitons. In this talk, I will discuss how much of this elegant structure survives away from flat space, focusing on AdS. As a first step, I will propose the fundamental building blocks of tree-level string amplitudes in AdS and then show how they are related via an AdS version of the KLT relations, whose kernel can be computed exactly. This structure not only significantly simplifies explicit calculations but also points to deeper algebraic and geometric structures to be uncovered.

Motivated by the observation that 2 + 2 = 4, we consider 4d N=2 SCFTs on S^2 x Sigma. On the one hand, reduction of a 4d theory T on a Riemann surface Sigma leads to a family F[T;Sigma] of 2d (2,2) unitary SCFTs, a 2d analog of the 4d theories of class S. On the other hand, reduction on S^2 yields a non-unitary two-dimensional CFT C[T] whose chiral algebra is the same as the one associated to T by the standard SCFT/VOA correspondence. This construction upgrades the vertex operator algebra to a full-fledged 2d CFT. What's more, it leads to a novel 2d/2d correspondence, a "2 + 2 = 4" analog of the "4 + 2 = 6" AGT correspondence: the S^2 partition function of F[T;Sigma] is computed by correlation functions of C[T] on Sigma. We discuss some structural aspects of this correspondence, and present an example where T is the (A1,A2) Argyres-Douglas SCFT and Sigma a four-punctured sphere. We also show how the elliptic genus of the F[T;Sigma] theories is captured by a TQFT on Sigma.

Irrational CFTs in 1+1d with a discrete spectrum and no conserved currents other than the stress-tensor are expected to be generic, unsolvable by standard methods, and hard to construct explicitly. In this talk, I will discuss a lattice model that realizes a candidate for such a CFT as a conformal phase of matter without fine-tuning. The model is constructed by coupling N ≥ 3 golden anyon chains together, preserving N copies of the Fibonacci non-invertible symmetry. I will briefly describe the N=2 case, where a weakly first-order phase transition (previously misidentified as an irrational CFT) occurs and some non-trivial (but rational) CFTs appear as unstable fixed points. For N = 3 we will show that a short RG flow occurs towards a stable CFT in the infrared with c~2.09. We indirectly argue that the CFT is irrational by comparing with a list of known rational CFTs with similar central charge. We will end with a discussion of other approaches that could be used to confirm/disprove our claim.

The AdS/CFT correspondence makes it possible in principle to study explicit black hole microstates using field theory techniques. In practice, this is still difficult because the field theory is only dual to gravity when it is strongly coupled. A more modest goal is to focus on supersymmetric black holes which have the minimal energy allowed by their other charges. The superconformal index suggests that many of these are protected from quantum corrections and can therefore be constructed at weak coupling. I will explain how one can identify candidates for black holes by searching the Hilbert space of ABJM theory. On general grounds, these should depend sensitively on trace relations at finite N. This principle, known as fortuity, was first established in a similar study of maximally supersymmetric Yang-Mills theory. I will show that similarities between the two theories extend to the quantitative level thereby allowing additional progress to be made without a brute force search.

Recently there has been significant interest in energy-energy correlators which measure the energy flux created at the point of collision by calorimeter-like detectors at asymptotically large distances. The primary building blocks of these observables are Average Null Energy operators (ANECs) which bear a strong resemblance to part of the charges associated to the symmetries of asymptotically flat spacetimes. In this talk, I will elucidate that relationship and show that calculable quantities that are more familiar in discussions of asymptotic symmetries and flat-space holography can be written in terms of energy-energy correlators, thereby allowing for natural connections to observables at particle experiments.