Cardy limit and large black holes; comments on generalizations and other examples

Indices and protected spectrum

Introduction: black hole thermodynamics; black holes in AdS; holographic viewpoint from (N=4 super) Yang-Mills

I will explain the physics of BPS black holes in AdS/CFT in 4 and 3 dimensions, focussing on the deconfined phases of the field theories.

Building upon recent progress in applying amplitude techniques to perturbative general relativity, we propose a closed-form formula for the conservative Hamiltonian of a spinning binary system at the 1st post-Minkowskian order. It is applicable for general spinning bodies with arbitrary spin multipole moments. It is linear in gravitational constant by definition, but exact to all orders in momentum and spin expansions. At each spin order, our formula implies that the spin-dependence and momentum dependence factorize completely. We compare our formula to a similar one derived in 2017 from a spinning test-body near a Kerr black hole and find perfect agreement.

Recently, all duality invariant α′ (alpha-prime)-corrections to the massless NS-NS sector of string theory on time-dependent backgrounds were classified and the form of their contribution to the action were calculated. In this talk we will see how to introduce matter sources in the resulting equations of motion in an O(d,d) covariant way. Then we show that either starting with the corrected equations and sourcing them with matter or considering corrections to the matter sourced lowest order equations give the same set of equations that defines string cosmology to all orders in α′. We also discuss perturbative and non-perturbative de Sitter solutions including matter, and explicitly show that de Sitter solutions are allowed non-perturbatively.

The work presented here explores the possibility of introducing non-Hermitian scalar and fermion mass terms, in addition to the usual Hermitian ones. The consistency of the resulting description requires a reworking of all the fundamental properties in Field Theory from the beginning, which is challenging but appears to be possible.

We study symmetry constraints on BPS surface defects in four-dimensional superconformal field theories, showing how supersymmetry imposes relations on anomaly coefficients. Turning to dynamics, we analyze a protected subsector of N=(2,2) surface defects that is captured by a two-dimensional chiral algebra. We discuss how to compute observables of interacting defects from the chiral algebra, including the aforementioned anomaly coefficients.

I present a method to expand in components four dimensional superconformal multiplets in N=1 and N=2 superconformal field theories. The method consists in constructing a differential operator for each descendant, which can then be applied on any correlator in superspace. In particular I show how the action on three-point functions can be considerably simplified. An interesting application of the formalism is the proof that N=2 spinning chiral primaries (also called ‘exotic’ primaries) cannot exist in any local SCFT. The interest in constraining this particular kind of operator stemmed from a result in the literature that ruled them out from a very large class of theories. I also discuss the role of the differential operators in the computation of superconformal blocks.

In this talk, based on [1906.07733] and [1907.11242] with Y. Jiang and S. Komatsu, we derive the first non-perturbative result for the structure constant of two determinant operators and a non-BPS single-trace operator of finite length in planar N=4 SYM. First, we introduce an effective theory for such correlators at zero coupling. The form of the result supports the interpretation of the three-point function as an overlap between an integrable boundary state, which we determine using symmetry and integrability, and the state describing the single-trace operator. Second, we use thermodynamic Bethe ansatz to derive a non-perturbative expression for such overlap. Finally, we discuss applications that could be addressed with these methods.

Not every effective theory of fields and gravitational interactions at low energy can be embedded into a consistent theory of gravity at short distances. I will discuss how fundamental properties of scattering amplitudes, such as unitarity and causality of the underlying fundamental theory, can be used to spot inconsistent theories of gravity at low-energy, and hence throw them in the so-called EFT ``swampland'’. I will focus on two main applications: the weak gravity conjecture for the physics of extremal black holes; and modified gravity theories such as Galileons, of interest for late-time cosmology.

The recent direct detection of gravitational waves marks the beginning of a new era for physics and astronomy with an opportunity the probe gravity at its most fundamental level and have already been used to successfully constrain or rule out many effective field theories relevant for cosmology. I will discuss the strengths and limitations of these constraints and explore other complementary approaches in segregating between various effective field theories.

Generalised Scherk-Schwarz reductions are a powerful tool to construct consistent truncations in Double and Exceptional Field Theories. Recently, it turned out that they are also closely related to Poisson-Lie T-duality. However, the most general form of Poisson-Lie T-duality, the dressing coset construction, can not be implemented in terms of a generalised Scherk-Schwarz ansatz. I will show that implementing it in generalised geometry leads to a natural extension of the generalised Scherk-Schwarz ansatz which comes with many new features: 1) Partial or full breaking of SUSY which allows to find many new examples of generalised Kähler or Calabi-Yau Manifolds. 2) Singular backgrounds with localised sources. 3) Localised vector multiplets while still resulting in consistent truncations.

We apply two non-perturbative methods, the numerical conformal bootstrap and supersymmetric localization, to four point functions of half-BPS operators in 3d maximally supersymmetric ABJM theory. This correlator is dual to scattering of gravitons and KK-modes in M-theory on AdS_4 x S^7, and determines the M-theory S-matrix in the flat space limit. Using localization, we compute OPE coefficients of certain protected operators exactly at small N and to all orders in 1/N at large N. We apply these analytic results to the numerical bootstrap in two ways. First, we find that numerical bootstrap bounds for these OPE coefficients are saturated by the analytic results, which allows us to read off all low-lying CFT data in the correlator, including for unprotected operators. Second, by imposing the analytical results we find precision islands in the space of certain quarter and eighth BPS OPE coefficients. This numerical data can be used to determine the M-theory S-matrix, which we confirm at leading order in large N.

Two-dimensional conformally invariant quantum field theories (CFTs for short) form a sprawling network of ideas connecting many areas of physics and mathematics. A particularly celebrated class are the rational CFTs. These are essentially characterised by having a completely reducible representation theory and only a finite number of inequivalent irreducible representations. Rational CFTs exhibit a number of extraordinary features, foremost being the Verlinde formula which determines correlation functions from certain transformation properties of the CFTs characters. Logarithmic CFTs by contrast are almost maximally awful in that their representation theory is necessarily not completely reducible and need not have finitely many inequivalent irreducible representations. I will present recent results on such logarithmic CFTs and argue that suitable generalisations of rational features exist, at least in certain cases. So things are not as bad as one might fear.

I will discuss two new areas of interest in scattering amplitudes: cluster adjacency and tropical geometry. The former describes how the analytic structure of planar amplitudes in N=4 Super Yang-Mills is controlled by mathematical objects called cluster algebras. The latter has been used to calculate amplitudes in the biadjoint phi^3 theory, which I will discuss briefly, but it also has implications for cluster adjacency.

Description:I will give a review of recent applications of conformal symmetry to perturbative calculations in Quantum Chromodynamics (QCD) by nexploiting the connection of physical theory to QCD at non-intege number of space-time dimensions at the critical point.

TeV hadron colliders provide the backbone for modern day particle physics. As a consequence, understanding QCD radiation is a vital step in linking theory with experiment. Over the last few decades a semi-classical treatment of radiation has been hugely successful; particularly the treatment given by Monte-Carlo event generators. However, as experiments demand greater precession, the traditional approaches struggle to keep up. Recently focus has been given to fully quantum approaches to QCD radiation by working directly with amplitudes rather than semi-classical probabilities. In my talk I will give an introduction to the current semi-classical approaches and where they fail. I'll then discuss some of the amplitude level techniques that are being developed. The amplitude techniques have broad application. I will give a case study of how these techniques can be used to elucidate coherence violation in QCD.