In this talk, I will describe new mathematical structures in the low-energy expansion of one-loop string amplitudes. The insertion of external states on the open- and closed-string worldsheets requires integration over punctures on a cylinder boundary and a torus, respectively. Suitable bases of such integrals will be shown to obey simple first-order differential equations in the modular parameter of the surface. These differential equations will be exploited to perform the integrals order by order in the inverse string tension, similar to modern strategies for dimensionally regulated Feynman integrals. Our method manifests the appearance of iterated integrals over holomorphic Eisenstein series in the low-energy expansion. Moreover, infinite families of Laplace equations can be generated for the modular forms in closed-string low-energy expansions.

I will present an introduction to anomalies and then discuss the recently discovered anomalies for supersymmetry.

Usually, scattering amplitudes in quantum field theory are computed perturbatively around a trivial background, but there are many reasons to be interested in non-trivial (or 'strong') background fields. These range from laser physics and QCD processes near heavy ion collisions to gravitational waves, conformal field theories and cosmology. Strong backgrounds also give us a way to test the robustness of new structures which have been discovered in scattering amplitudes. I will discuss perturbative Yang-Mills theory on a particularly simple (but important) background known as a plane wave, and consider a very basic observable: the scattering amplitude for a gluon to flip helicity as it crosses the background. This 'helicity flip' amplitude is a loop effect, and the leading result for Yang-Mills (and QCD) can be expressed compactly using a background-dressed version of the spinor helicity formalism (a method for freely specifying on-shell kinematics). Time permitting, I may also make some remarks about higher-point gluon amplitudes in the plane wave background, or the version of this story for gravity.

I will start by motivating the recent interest in non-relativistic gravity and strings, and introduce the basics of Newton-Cartan geometry. Newton-Cartan (NC) geometry was introduced more than 90 years ago in order to find a geometric formulation of Newtonian gravity. This geometry (including recent novel generalisation and extensions) has gained renewed interest as it appears in a variety of settings in modern theory involving gravity, string theory and holography. I will then talk about recent work on an action principle for non-relativistic gravity, including its Newtonian limit. This requires a new notion of NC geometry, which naturally arises in a covariant 1/c expansion of general relativity, with c being the speed of light. The corresponding non-relativistic truncation of general relativity goes beyond Newtonian gravity and is able to correctly describe gravitational time dilation. Finally, I will discuss the relevance and appearance of non-relativistic geometry in connection to non-relativistric string theory and holography.

Temperature manifests itself within quantum field theories (QFTs) and conformal field theories (CFTs) via an identification of points in the Euclidean-time direction, which differ by an integer multiple of 1/T. Today, I will talk about finite-temperature path integrals for general QFTs and for two-dimensional CFTs (2d CFTs) on the compact two-torus. By definition, the latter path integrals are modular invariant. I will discuss why, propose an extension of the modular group from SL_2(\Z) to GL_2(\Z), introduce the notion of modular forms with poles, and discuss general properties of modular forms with and without poles that are defined on the extended group GL_2(\Z). Finally, I will discuss how this extension to GL_2(\Z) may introduce a new source of anomalies/consistency conditions in 2d CFTs (and beyond).

Renormalization group methods have been used for almost 50 years to obtain results for critical exponents of conformal field theories (CFTs), while relying on assumptions and approximations that are not rigorously justified. More recently, the numerical conformal bootstrap, a fully nonperturbative method, has proven to be very powerful in calculating critical exponents and other physical observables of unitary CFTs. In this talk we will review the numerical conformal bootstrap method and discuss its applications to 3D CFTs relevant for continuous phase transitions observed in various experiments.

We consider α′ corrections to four-point correlators of half-BPS operators in N = 4 super Yang-Mills theory in the supergravity limit within the context of AdS/CFT. By demanding the correct behaviour in the flat space limit, we find that the leading (α′)^3 correction to the Mellin amplitude is fixed for arbitrary charges of the external operators. We consider double-trace operators and observe striking patterns in the α′ corrections to the spectra which hint at their common ten-dimensional origin. By extending the observed patterns and imposing them at order (α′)^5 we are able to reproduce recent results for certain correlators as well as deduce some new results.

I will talk about the recent quite interesting article by Maldacena, in which he writes on the subject of the traversable wormholes. The most interesting thing that needs to be pointed out here are the way that wormholes are stabilised without the addition of the exotic matter while the theory that describes them is still Einstein gravity, with Maxwell theory and charged massless fermion, since wormholes without the addition of the exotic matter have been known in the higher derivative theories. The wormhole is made possible by fermions that give rise to negative Casimir-like energy and by being a long wormhole which does not lead to causality violations. https://arxiv.org/abs/1807.04726

I would like to discuss a class of three-dimensional topological field theories called Reshetikhin-Turaev theories. Examples are Chern-Simons theories with compact gauge group. There are no point-like observables in these theories, and one typically considers line-observables, called Wilson lines. However, one can also discuss observables associated to surfaces. We will see how to describe such observables in Reshetikhin-Turaev TQFTs and look at some applications.

In this talk, I will connect, via tree-level double copy, any massless string amplitudes with QFT amplitudes given by Cachazo-He-Yuan (CHY) formula. This can be derived by a detailed study of integration-by-part (IBP) reduction of string integrands. As an application, we consider general multitrace integrands of heterotic string amplitudes. The new technology generates a recursive expansion of the heterotic string amplitudes in terms of those with fewer gravitons and traces, where the kinematic coefficients are building blocks for BCJ numerators of the (DF)^2+YM+phi^3 theory. Finally, we give a generic CHY integrand for multitrace (DF)^2+YM+phi^3 amplitudes, which reproduce the corresponding heterotic string amplitudes after double copy with a single-valued Z-theory.

We study the leading and next-to-leading eikonal phase in the context of AdS/CFT. In the bulk side, we compute the phase shift of a highly energetic particle traveling in the background of an asymptotically AdS black hole. In the dual CFT, the phase shift is related to a four point function in the Regge limit. The black hole mass is translated to the ratio between the conformal dimension of a heavy operator and the central charge. This ratio serves as a useful expansion parameter; its power measures the number of stress tensors appearing in the intermediate channel. The leading eikonal phase shift in 4d holographic CFTs can be computed using conformal Regge theory while the computation of the next-to-leading order eikonal phase shift relies on a new universal formula for the lowest-twist OPE of double-trace stress-tensors with two scalar operators. These OPE coefficients are consistent with the second-order phase shift as well as anomalous dimensions obtained in AdS black holes in the lightcone limit. In relations to the idea of “eikonalization” of the stress-tensor sector in holographic CFTs, we comment on hints of a structure similar to the vacuum Virasoro block in 2d CFT.

Hydrodynamic excitations corresponding to sound and diffusive modes in fluids are characterised by gapless dispersion relations. In the hydrodynamic gradient expansion, their frequencies are represented by infinite power series in spatial momenta. I will discuss how the introduction of a new concept of the hydrodynamic complex spectral curve in the space of complexified frequency and spatial momentum—the concept otherwise known from algebraic geometry---can be used to prove general properties about hydrodynamics, including its finite radius of convergence. When the infinite series are resummed, they exhibit a fascinating, recently-discovered phenomenon of pole-skipping, which enables us to analyse the underlying, microscopic quantum many-body chaos in the system. Throughout my talk, I will use gauge-gravity duality as a tool to explicitly show these phenomena in holographic systems and discuss what their implications are for the dual gravity theory.

Fractional quantum Hall (FQH) states are topologically ordered. Additionally, FQH states support a collective neutral excitation known as the Girvin-MacDonald-Platzman (GMP) mode. Certain features of this mode are independent of the microscopic details. The objective of the talk is to construct an effective theory includes both topological properties and the massive GMP mode. The theory reproduces the universal properties of chiral lowest Landau level (LLL) FQH states which lie beyond the TQFT data, such as the projected static structure factor and the GMP algebra of area-preserving diffeomorphisms. The dynamics of the mode is described by a fluctuating rank-2 symmetric, positive-definite tensor, which leads to a natural geometric (or gravitational) interpretation of the GMP mode.

This talk presents the progress made in my research via the introduction of effective field theories (EFTs) into post-Newtonian (PN) gravity. These have been put forward in the context of gravitational waves (GWs) from the compact binary inspiral. The setup and the strategy of a multi-stage EFT framework, which is deployed for the PN binary inspiral problem, is outlined. I then present in more detail the study of two effective theories at the intermediate scales of the problem. First, the EFT for a single rotating compact object is considered, from which I proceed to the EFT of a compact binary system, viewed as a composite particle with internal binding interactions. I conclude with the prospects of building on the field, and using further modern field theory insights and tools, to address the study of GWs, as well as to expand our fundamental understanding of QFTs and gravity theories at all scales.

Supersymmetric extensions of conformal gravity have been known for a long time. In four dimensions, N=4 conformal supergravity is the maximally supersymmetric theory of this type. Although its field representation and the non-linear transformations rules were derived more than 30 years ago, no invariant action had been constructed so far. We present the most general class of actions which turns out to be characterised by a holomorphic function. This deviates from the non-maximally supersymmetric cases where the action is unique. Meanwhile, elaborate loop computations have indicated that N=4 Poincare supergravity diverges at four loops, and the divergence is believed to be related to the presence of a potential one-loop anomaly in the duality symmetry of the theory. We argue that one of the constructed conformal actions, after gauge fixing the conformal symmetries and carefully eliminating auxiliary fields, can be used as a finite supersymmetric counterterm that cancels the anomalous contribution of the one-loop graphs in the Poincare theory.

The 1/2 BPS and regular LLM geometries are formed from the backreaction of a large number of D-branes on AdS_5 x S^5. The dual N=4 SYM operator to this configuration, and excitations thereof, thus lie outside of the planar limit of the theory. Explicitly the operators dual to these geometries are Schur polynomials labelled by a Young diagram with O(N^2) boxes and excitations of this configuration are restricted Schur polynomials obtained by adding boxes (and restriction labels) to this diagram. A special class of these geometries are labelled by Young diagrams with O(1) well separated corners. In the large N limit excitations localised at any one of these corners only mix with each other which is a major simplification. A recent proposal has argued that the large N dynamics of these operators is isomorphic to that of planar N=4 SYM and thus represents an integrable subsector of N=4 SYM. In this talk this proposal is reviewed and aspects of the weak and strong coupling evidence presented.

After a summary of current status of experimental results in particle physics, including the presentation of what I call the LHC paradox, I will discuss briefly how colliders were indispensible in arriving at this point of the journey. After this I would discuss what the next steps are: as to where do we go from here in the story of collider physics. If time is left, I will discuss some of the issues that the future colliders can address , by taking examples from the known unknowns, viz. in the framework of particular BSM models and also the unknown unknowns viz the model independent approach.

In this seminar I will discuss a recently-found class of RG flows in four dimensions exhibiting enhancement of supersymmetry in the infrared, which provides a lagrangian description of several strongly-coupled N=2 SCFTs. The procedure involves starting from a N=2 SCFT, coupling a chiral multiplet in the adjoint representation of the global symmetry to the moment map of the SCFT and turning on a nilpotent expectation value for this chiral. We show that, combining considerations based on 't Hooft anomaly matching and basic results about the N=2 superconformal algebra, it is possible to understand in detail the mechanism underlying this phenomenon and formulate a simple criterion for supersymmetry enhancement.