Main Session

We systematically explore the space of renormalization group flows of four-dimensional N=1 superconformal field theories (SCFTs) triggered by relevant deformations, as well as by coupling to free chiral multiplets with relevant operators. In this way, we classify all possible fixed point SCFTs that can be obtained from certain rank 1 and 2 supersymmetric gauge theories with small amount of matter multiplets, identifying 7,346 inequivalent fixed points which pass a series of non-trivial consistency checks. This set of fixed points exhibits interesting statistical behaviors, including a narrow distribution of central charges (a, c), a correlation between the number of relevant operators and the ratio a/c, and trends in the lightest operator dimension versus a/c. The ratio a/c of this set is distributed between 0.7228 and 1.2100, where the upper bound is larger than that of previously known interacting SCFTs. Moreover, we find a plethora of highly non-perturbative phenomena, such as (super)symmetry enhancements, operator decoupling, non-commuting renormalization group flows, and dualities. We especially identify amongst these fixed points a new SCFT that has smaller central charges (a, c) = (633/2000, 683/2000) than that of the deformed minimal Argyres-Douglas theory, as well as novel Lagrangian duals for certain N=1 deformed Argyres-Douglas theories.

Selection rules are one of the most basic manifestations of symmetry in a quantum mechanical system. Standard selection rules are useful for proving the vanishing of certain scattering amplitudes to all orders in perturbation theory. However, there are also examples of scattering amplitudes that vanish at low orders in perturbation theory, but are non-zero at higher orders. In this talk I will introduce a generalized notion of selection rules that can account for such phenomenon. These selection rules do not have an underlying symmetry explanation in field theory, but they do have one in string theory.

I will discuss the modular properties of certain physical observables in N=4 super Yang-Mills theory (SYM). These observables include the correlation functions of half-BPS local operators, with and without the presence of line defects. To simplify the problem, we consider the integrated version of these correlators, where the spacetime dependence is integrated out using specific measures. These are known as integrated correlators. We will demonstrate that these integrated correlators can be represented as certain lattice sums, which manifest the modular properties of N=4 SYM and provide exact results for the integrated correlators at any finite coupling.

Recently, the conformal bootstrap was adapted to produce rigorous, new and strikingly powerful bounds on the spectra of hyperbolic manifolds. I will review these developments and explain what they teach us about conformal field theory.

Black holes with two charges in string theory are singular due to vanishing horizon area at extremality. Two seemingly contradictory resolutions are available in the literature. On one hand, it has been argued that higher-derivative effects create a string-sized extremal horizon. On the other hand, it has been argued that before such a small black hole even forms, there is a transition to a winding condensate and eventually a gas of strings. We show that, with some modifications, these two perspectives are compatible, but correspond to different observables.

I will discuss how generic quantum corrections lift the moduli space of BPS branes in 4d N=1 scale-separated solutions like DGKT. This means that there is a tension between this scenario and the WGC for membranes, which demands the existence of an exactly extremal brane.

I am going to talk on our recent work revisiting the path-integral approach to the wave function of the universe by utilizing Lefschetz thimble analyses and resurgence theory. The traditional Euclidean path-integral of gravity has the notorious ambiguity of the direction of Wick rotation. In contrast, the Lorentzian method can be formulated concretely with the Picard-Lefschetz theory. Yet, a challenge remains: the physical parameter space lies on a Stokes line, meaning that the Lefschetz-thimble structure is still unclear. Through complex deformations, we resolve this issue by uniquely identifying the thimble structure. This leads to the tunneling wave function, as opposed to the no-boundary wave function, offering a more rigorous proof of the previous results. Further exploring the parameter space, we discover rich structures: the ambiguity of the Borel resummation of perturbative series around the tunneling saddle points is exactly cancelled by the ambiguity of the contributions from no-boundary saddle points. This indicates that resurgence works also in quantum cosmology, particularly in the minisuperspace model. This talk is based on a collaboration with Hiroki Matsui, Kazumasa Okabayashi and Takahiro Terada (arXiv:2402.09981).

I will review a notion of quantum chaos for BPS states in supersymmetric holographic systems, first proposed by Lin, Maldacena, Rozenberg, and Shan. We explore this proposal across various BPS sectors in N=4 SYM theory and find evidence suggesting that sectors described by horizonless geometries exhibit only weak chaos, while the phenomenon of fortuity implies that the sector corresponding to supersymmetric black holes is strongly chaotic. In the second part of the talk, I will introduce an SYK-like toy model that helps demonstrate the relationship between chaos and fortuity.

We explicitly reconstruct both the worldsheet and the target space embedding of closed (topological) strings purely from the dual gauge theory Feynman diagrams. We encounter the "next simplest gauge-string duality", between a two-matrix integral and mirror worldsheet theories, valid to all orders in the genus expansion. We show how the correlators of the A-model worldsheet theory precisely reproduce the perturbative gauge theory observable by localizing to particular covering maps of the Riemann sphere. This provides a fully microscopic picture of open/closed string duality for a topological subsector of the full AdS/CFT correspondence.

For string backgrounds with known exact worldsheet theory descriptions, ordinary string perturbation theory can be employed to study their observables such as string spectrum and scattering. However, many of interesting string backgrounds, including AdS and flux compactifications, lack such descriptions, posing challenges in understanding their stringy physics. Since these backgrounds are typically described as solutions to low-energy supergravity theory, having a string-theoretic counterpart to this field theory is desirable. In this talk, we discuss how string field theory provides such a framework, along with its limitations. Despite such limitations, we illustrate its practical utility in examining physical observables, particularly in examples such as AdS and flux compactifications.

We will discuss general properties of perturbative and large-$N$ RG fixed points and analyze broad classes of deformations of the $O(N)$ model. In studying fixed points with exactly marginal operators and classifying large-$N$ field contents in theories with increasing numbers of operators, we will witness what narrow separation sets apart the questions whose answers generalize straightforwardly from those which become unfathomably difficult as the amount of symmetry in a system is incrementally lowered.

While we believe we know everything about Virasoro minimal models, the renormalization group flows among them, in particular non-unitary cases, are largely unknown. Based on the study of non-invertible symmetries, we propose there exist infinitely many new renormalization group flows between Virasoro minimal models M(kq+I,q) -> M(kq−I,q). They vastly generalize the previously proposed ones k=I=1 by Zamolodchikov, k=1,I>1 by Ahn and Lassig, and k=2 by Dorey et al. All the other Z2 preserving renormalization group flows sporadically known in the literature (e.g. M(10,3) -> M(8,3) studied by Klebanov et al) fall into our proposal (e.g. k=3,I=1). We claim our new flows give a complete understanding of the renormalization group flows between Virasoro minimal models that preserve a modular tensor category with the SU(2)q−2 fusion ring. The talk is based on arXiv:2407.21353 in collaboration with Takahiro Tanaka.

I will make a comment on how to generalize Saad's wormhole to higher dimensions.

Gravitational anomalies in six dimensions can be eliminated through the Green-Schwarz-Sagnotti mechanism. This is realised in type IIB string theory with orientifold projections and many non-perturbative generalisations. The supersymmetric counter-term necessary to cancel the anomaly is known for a single tensor multiplet (type I string) and for the Yang-Mills part with any number of tensor multiplets. We have written the R^2 type counter-term for an arbitrary number of tensor multiplets by introducing a map to the off-shell dilaton-Weyl multiplet.

Tidal Love numbers quantify the deformability and dissipative properties of compact gravitating objects. However, due to the nonlinearity of gravity, they undergo renormalization group running even in classical GR. In this talk I will explain some exact results about their running, which can be extracted by matching calculations of scattering amplitudes in black hole perturbation theory and point-particle effective theories. Due to the universality of EFT, the results have applications to the physics of black holes, neutron stars, binaries, and even quantum decoherence. For the specific case of black holes, our matching calculation also provides the precise values of both static and dynamical Love numbers in various dimensions.

We revisit the holographic description of 6d (2,0) theories from M-theory, with special focus in clarifying several features regarding the relative structure of the theories of Type D, holographically dual to M-theory on AdS7 x RP4. In particular, we give a holographic derivation of the 7d topological sector responsible for the relative structure of the 6d (2,0) theories of D-type. We relate the Freed-Hopkins analysis on M-theory on non-orientable spaces to the anomaly polynomial for 6d (2,0) SCFTs of type D. The Freed-Hopkins integrality constraint for M-theory on non-orientable manifolds translates in this specific background into the subtraction procedure identified by Intriligator and Yi independently, in their seminal papers on the 6d anomaly polynomials, thus providing a profound consistency check.