We propose the Gauge Theory Bootstrap, a method to compute the pion S-matrix that describes the strongly coupled low energy physics of QCD and other similar gauge theories. The method looks for the most general S-matrix that matches at low energy the tree level amplitudes of the non-linear sigma model and at high energy, QCD sum rules and form factors. We compute pion scattering phase shifts for all partial waves with angular momentum $\ell<=3$ up to 2 GeV and calculate the low energy ChiPT coefficients. This is a theoretical/numerical calculation that uses as only data the pion mass $m_\pi$, pion decay constant $f_{\pi}$ and the QCD parameters $N_c=3$, $N_f=2$, $m_q$ and $\alpha_s$. All results are in reasonable agreement with experiment. In particular, we find the $\rho(770)$, $f_2(1270)$ and $\rho(1450)$ resonances and some initial indication of particle production near the resonances. The interplay between the UV gauge theory and low energy pion physics is an example of a general situation where we know the microscopic theory as well as the effective theory of long wavelength fluctuations but we want to solve the strongly coupled dynamics at intermediate energies. The bootstrap builds a bridge between the low and high energy by determining the consistent S-matrix that matches both and provides, in this case, a new direction to understand the strongly coupled physics of gauge theories. Based on work with Martin Kruczenski.

I will discuss a novel construction of field theories based on the idea that one has only a half boson degree of freedom per lattice site. Basically, instead of having a pair of canonical conjugate commuting variables at each site, one has only one degree of freedom and the non-trivial commutators arise from connections to the nearest neighbors. The construction is very similar to staggered fermions and naturally produces gapless systems with interesting topological properties. When considering gauging discrete translations on the phase space in one dimensional examples, one gets interesting critical spin chains, examples of which include the critical Ising model in a transverse magnetic field and the 3-state Potts model at criticality. I will explain how these staggered boson variables are very natural for describing non-invertible symmetries. These non-invertible symmetries are useful to describe the critical properties of these non-trivial spin chains. Models in higher dimensions obtained this way can automatically produce dynamical systems of gapless fractons.

In this talk, I will discuss a connection between the ANEC (Averaged Null Energy Condition) operator and monotonicity of the renormalization group. In particular, I will show how the 2d c-theorem and 4d a-theorem can be derived using the ANEC. This derivation relies on contact terms appearing in specific ANEC correlators. I will also review a new infinite set of constraints that can be derived from the ANEC in 2d QFT. This program hints at a more general role for light-ray operators in QFT, which I will argue for.

Carroll symmetries were introduced many years ago by Levy-Leblond and Gupta as a possible contraction of the Lorentz symmetries in which effectively the speed of light is sent to zero. The name was inspired by the bizarre property that Carroll particles cannot move. After many years of silence Carroll symmetries have returned to the stage since they have been recognized as symmetries that do occur in several special situations such as the horizon of a black hole. In this presentation I will discuss some of the basic properties and mysteries of Carroll symmetries.

de Sitter spacetime admits distinct Friedmann-Robertson-Walker foliations with cosh, sinh and exponential time evolution laws. In three or more spacetime dimensions, these foliations have respectively positive, negative and vanishing spatial curvature. In two spacetime dimensions, by contrast, there is no spatial curvature, and all three evolution laws allow spatial sections with S^1 topology and a freely specifiable spatial circumference parameter. We identify geometrically preferred quantum states for a massive scalar field on these locally de Sitter 1+1 cosmologies, some singled out by adiabatic criteria, others induced from the Euclidean vacuum by a quotient construction. We show how a comoving quantum observer, modelled as an Unruh-DeWitt detector, can distinguish these states by local measurements. (Joint work with Vladimir Toussaint, 2304.10395)

The Swampland program aims at formulating a complete set of criteria in order to identify theories that can be uplifted in the UV to a theory of quantum gravity. The distance conjecture in particular diagnoses viable low energy effective theories by examining their breakdown at infinite distance in their parameter space. At the same time, infinite distance points in parameter space are naturally intertwined with string dualities and in particular T-duality. In this talk, we will show that this relation becomes much richer and intricate when the internal space is curved or supported by fluxes. Consistency of T-duality then leads us to suggest an extension to the Swampland distance conjecture. This work is in collaboration with Thomas Raml and Dieter Lüst.

Double-scaled SYK (DSSYK) is a model with interesting dynamics, and many known exact results. Yet, the gravitational behavior of the system is not fully understood. I will discuss the reasoning behind a suggested connection between DSSYK and de Sitter holography. We will mention the general form of the correspondence as well as the mapping of parameters between the two sides. On the SYK side we consider two copies of DSSYK at infinite temperature with an equal energy constraint. We will discuss explicitly the two-point function in double-scaled SYK and compare it to de Sitter.

In holographic duality, a higher dimensional quantum gravity system is equivalent to a lower dimensional conformal field theory (CFT) with a large number of degrees of freedom. In this talk, I will introduce a framework to describe using the CFT how geometric notions in the gravity system, such as spacetime subregions, different notions of times, causal structure, and spacetime connectivity, emerge in the semi-classical limit.

I will discuss the physics of high energy, many-particle states from two complementary perspectives. First, I will present a new method for using data from conformal field theories to compute observables in more general QFTs, which can be used to numerically study many properties of many-particle states. Then I will consider an analytic approach to a particular set of these states, those near threshold, where many features become largely theory-independent.

In this talk, I will discuss correlation functions in 6d (2, 0) theories of two 1/2-BPS operators inserted away from a 1/2-BPS surface defect. In the large central charge limit the leading connected contribution corresponds to sums of tree-level Witten diagram in AdS7×S4 in the presence of an AdS3 defect. I will show that these correlators can be uniquely determined by imposing only superconformal symmetry and consistency conditions, eschewing the details of the complicated effective Lagrangian. I will present the explicit result of all such two-point functions, which exhibits remarkable hidden simplicity.

In recent years we've greatly expanded our understanding of entanglement in many-body quantum systems; both how it behaves in ground states, and how it grows out-of-equilibrium. While entanglement is very difficult to measure in experiments, it has nevertheless driven progress in 1) the classification of quantum phases of matter and 2) strategies for efficiently simulating many-body systems on classical and quantum computers. I will review some recent progress in these directions. Along the way I will summarise some older results on how entanglement grows in many-body systems, briefly highlight some connections to holography, and present a conjecture about the asymptotic computational difficulty of calculating transport in many-body systems.

This talk is about our latest work in [arXiv:2311.18302]. We shall show how one can define novel gauge-theoretic Floer homologies of four, three and two-manifolds that are associated with Vafa-Witten, Hitchin and complexified BF configurations, respectively, from the physics of a certain topologically-twisted 5d N=2 gauge theory. Via topological invariance and a 5d “S-duality”, we shall derive novel Atiyah-Floer correspondences of these gauge-theoretic Floer homologies which relate them to symplectic intersection Floer homologies of Higgs bundles, and a web of relations involving their loop/toroidal group generalizations and their Langlands dual. Lastly, through a soliton string theory interpretation of the 5d theory, we shall derive a Fukaya-Seidel type A-infinity category of Hitchin configurations on three-manifolds and its Atiyah-Floer correspondence. We therefore furnish purely physical realizations and generalizations of the mathematical conjectures and constructions of Haydys [1], Wang [2] and Abouzaid-Manolescu [3], and more.

We study Chern-Simons theories at large N with either bosonic or fermionic matter in the fundamental representation. We will show that for smooth conformal line operators, their spectrum and shape dependence can be effectively bootstrapped using minimal inputs.

I will explain how to describe form factors of single-trace half-BPS operators in planar N=4 super Yang Mills theory using the T-dual Wilson loop picture. After reviewing earlier results for operators in the stress-tensor multiplet, I will present the dual Wilson loop description for the so-called MHV form factors of half-BPS operators. The general proposal relates these form factors to the matrix elements of a null periodic super Wilson loop with outgoing states composed of zero-momentum scalars. I will present perturbative tests of this description at weak coupling. I will then explain how to obtain exact result at finite coupling in the collinear limit using the Wilson loop Operator Product Expansion. I will conclude with general comments and speculations about form factors of unprotected operators such as the Konishi operator.

I will discuss some of the recent developments in the Krylov complexity. In particular, I will focus on the applications of the Krylov basis techniques to the modular Hamiltonian evolution and I will discuss a new angle on entanglement entropy in QCD at high energies. Based on arXiv:2306.14732 [hep-th] and work in progress.

I will discuss a connection between harmonic analysis on hyperbolic n-manifolds and conformal field theory in n-1 dimensions. Used in one direction, this connection leads to new spectral bounds on hyperbolic manifolds. Used in the other direction, it offers a new viewpoint on the spectra data of conformal field theories.

We will consider perturbations of 2D CFTs by multiple relevant operators. The massive phases of such perturbations can be labeled by conformal boundary conditions. Cardy's variational ansatz approximates the vacuum state of the perturbed theory by a smeared conformal boundary state. In this talk we will discuss the limitations and propose generalisations of this ansatz using both analytic and numerical insights based on TCSA. In particular we analyse the stability of Cardy's ansatz states with respect to boundary relevant perturbations using bulk-boundary OPE coefficients. We show that certain transitions between the massive phases arise from a pair of boundary RG flows. The RG flows start from the conformal boundary on the transition surface and end on those that lie on the two sides of it. As an example we work out the details of the phase diagram for the Ising field theory and for the tricritical Ising model perturbed by the leading thermal and magnetic fields. Based on arXiv:2306.13719.

**Send email to jeremy.mann@kcl.ac.uk for link to online seminar.** In general relativity, spacetime metrics satisfy the Einstein equations, which are wave equations in the harmonic gauge. The Cauchy problem for the vacuum Einstein equations has been well-understood since the work of Choquet-Bruhat. For an initial data set satisfying the vacuum constraint equations, there exists a solution to the vacuum Einstein equations and it is geometrically unique in the domain of dependence of the initial surface. On contrast, the initial boundary value problem (IBVP) has been much less understood. To solve for an vacuum metric in a region with time-like boundary, one needs to impose boundary conditions to guarantee geometric uniqueness of the solution. However, due to gauge issues occurring on the boundary, there has not been a satisfying choice of boundary conditions. In this talk I will discuss obstacles in establishing a well-defined IBVP for vacuum Einstein equations and the geometric uniqueness problem. Then I will talk about an existence and geometric uniqueness result in a joint work with Michael Anderson.

A ’t Hooft loop is a typical disorder operator defined in any gauge theory that can be studied by a combination of holography, localization and integrability. After reviewing the quantum mechanics magnetic monopoles, I will describe how integrability and Bethe ansatz can help to study ’t Hooft loops in the N=4 super-Yang-Mills theory.