Quantum Fields and Strings

I'll discuss four-point functions of CFT operators with infinite scaling dimension, which arise ubiquitously in both holographic and non-holographic CFTs in general dimension, as well as in the flat space limit of rigid QFTs on AdS. The space of these correlators is poorly understood, due to both their computational complexity and inaccessibility through standard bootstrap techniques. To navigate these challenges, I'll introduce a rigorous framework for extracting well-defined ``maximally heavy observables,'' which are analogous to intrinsic quantities describing statistical systems in the thermodynamic limit. These observables are highly constrained by crossing symmetry and unitarity, and shed light on the emergence of bulk locality through dynamical phase transitions. I'll relate this framework to torus partition functions at large central charge, and work out illustrative examples in generalized free theories and the four-point function of maximal giant gravitons in planar $\mathcal{N}=4$ SYM.

Defects and boundaries play an important role in a wide range of physical contexts, from particle physics to critical phenomena. In this talk, I will discuss how bulk symmetries can be realized in subtle ways in the presence of such impurities, introducing the concepts of symmetry reflecting defects and defect anomalies. I will focus on two main applications. First, I will demonstrate how these symmetry considerations can impose strong constraints on the long-distance dynamics. Second, I will show how they provide a natural explanation for scattering processes whose outgoing states appear to carry unusual quantum numbers. These phenomena can be understood and systematically predicted from topological considerations, in a variety of examples including massive theories.

Interacting fermions exhibit a rich landscape of surface defects. We investigate novel surface critical phenomena in systems governed by the three-dimensional Gross–Neveu–Yukawa CFT. In particular, we obtain exact infrared solutions for a class of defect renormalization group flows and demonstrate how various fermionic anomalies are encoded in the resulting surface dynamics. We also comment on the emergent topology and geometry in the defect coupling space.

Inflation may have occurred at energies up to 10^16 GeV, far beyond the reach of any terrestrial collider. The "cosmological collider" program seeks to extract the mass spectrum and spin content of particles present during inflation from non-Gaussian correlators. Forthcoming large-scale structure surveys target the critical f_NL ~ O(1) threshold, and future 21 cm observations could in principle approach the gravitational floor at f_NL ~ O(0.01). However, isolating these primordial signals places a premium on robust theoretical templates. Significant progress has been made in computing certain tree-level models, but important physical scenarios require going beyond tree level. Whenever the heavy particle coupled to the inflaton carries a conserved quantum number, such as gauge charge or fermion number, the leading contribution to the bispectrum first arises at one loop. This makes loop-level computations essential rather than a mere perturbative refinement. In this talk, I describe how techniques from tropical geometry, originally developed for multi-loop Feynman integrals in flat space, can be adapted to evaluate loop-level Witten diagrams in de Sitter space in complete generality for the first time. I present results for the one-loop bubble bispectrum generated by the derivative portal (d phi)^2 sigma^2 at fully general kinematics and masses, as well as the one-loop triangle diagram. I compare the resulting templates with CMB data. We expect these methods to be applicable to a broad range of cosmological models.

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.