In this talk, I will discuss the construction of 2d (0,2) supersymmetric gauge theories corresponding to the 18 smooth Fano 3-folds and the families of Y^(p,k)(CP1xCP1) and Y^(p,k)(CP2) Sasaki-Einstein 7-manifolds. These 2d (0,2) gauge theories can be considered as the worldvolume theories of D1-branes probing toric Calabi-Yau 4-folds. The talk will illustrate how the map between gauge theory and the corresponding geometry is considerably simplified by a Type IIA brane configuration called brane brick models.

I will discuss positivity bounds on EFT coefficients in theories where Lorentz boosts are spontaneously broken. The well-known S-matrix argument from the Lorentz-invariant scenario does not straightforwardly generalize to this case. Instead the analytic properties of the retarded Green’s function of conserved currents (or of the stress-energy tensor) will be used, and the theory will be assumed to become conformal in the UV. The method is general and applicable to both cosmology and condensed matter systems. As a concrete example we will consider the EFT of conformal superfluids, which describes the universal low-energy dynamics of CFTs at large U(1) charge, and we will derive inequalities on the coefficients of the operators, in three spacetime dimensions, at NLO and NNLO.

The worldsheet theory of string backgrounds is a CFT with zero central charge. This is the definition of on-shell string theory. In off-shell string theory, on the other hand, conformal invariance on the worldsheet is explicitly broken, and the worldsheet theory is therefore a QFT rather than a CFT, with a UV cutoff. In this talk, I will explain Tseytlin's prescriptions for constructing classical (tree-level) off-shell effective actions and provide a general proof, using conformal perturbation theory, that it gives the correct equations of motion, to all orders in perturbation theory and $\alpha'$. I will also show how Tseytlin's prescriptions are equivalent to quotienting out by the gauge orbits of a regulated moduli space with "n" operator insertions. I will also explain how Tseytlin's prescriptions encode the correct prescription for the Lorentzian S-matrix in which case we obtain Feynman's $i\varepsilon$ prescription for the internal poles. Finally, I will explain how the classical off-shell string action was used by Susskind and Uglum to calculate the tree-level black hole entropy on a conical manifold in Rindler background. Time permitting, I will present very recent upcoming work on a closed-form expression for a generalized Tseytlin (GT) operator that eliminates all spurious tadpoles from higher curvature couplings on the worldsheet. This allows us to study its action on correlations functions of scalar primaries and descendants with arbitrary conformal dimensions.

I will review how non-linearities can allow for screening solar-system scales from non-tensorial gravitational polarizations, focusing on the case of scalar-tensor theories with derivative self-interactions (K-essence). I will then present fully relativistic simulations in these theories in 1+1 dimensions (stellar oscillations and collapse) and 3+1 dimensions (binary neutron stars), showing how to avoid breakdowns of the Cauchy problem that have affected similar attempts in the past. I will show that screening tends to suppress the (subdominant) dipole scalar emission in binary neutron star systems, but that it fails to quench monopole scalar emission in gravitational collapse, and quadrupole scalar emission in binaries.

Mixed anomalies and generalized symmetries have proved to be useful in providing non-trivial constraints on the dynamics of quantum field theories (QFTs). A natural question is whether these are related in any way to certain supersymmetric partition functions or indices, which have also been used extensively to study the dynamics of QFTs. In this talk, we address this question in the context of 3d N≥3 gauge theories using the superconformal index. In particular, using the index we are able to detect mixed anomalies involving discrete 0-form global symmetries, and possibly a 1-form symmetry. The effectiveness of this method is demonstrated via several classes of theories, including Chern-Simons-matter theories, the T(SU(N)) theory of Gaiotto-Witten and variants of the Aharony-Bergman-Jafferis (ABJ) theory with the orthosymplectic gauge algebra. Gauging appropriate global symmetries involved in mixed anomalies of some of these models and using constructions available in the literature, we obtain various interesting theories with two-group structures or non-invertible symmetries.

In some ways the ocean acts like a topological insulator. There are chiral edge modes, localised at the coast, that go clockwise in the Northern hemisphere and anti-clockwise in the Southern hemisphere. I’ll describe these features and explain how this can be understood in terms of something more familiar to high energy physicists. I’ll show that the equations that govern the long-time dynamics of the ocean can be recast as a Maxwell-Chern-Simons theory.

Tremendous progress has been achieved during the last years in bootstrapping conformal correlators at strong coupling using analytical bootstrap methods and the AdS/CFT correspondence. In particular, the development of Lorentzian inversion formulae revealed helpful in reconstructing four-point functions. In this talk I will present how this technology can be adapted to defect setups in order to compute scalar two-point functions in the presence of a conformal defect in the strong-coupling regime. We derived a dispersion relation that allows to efficiently generate elegant closed-form expressions for a variety of setups, and in particular we apply this method to two-point functions of single-trace half-BPS operators in the presence of the supersymmetric Wilson line defect in 4d N=4 SYM, using minimal input from holography.

In 1968, D. Atkinson proved in a series of papers the existence of functions satisfying all known constraints of the S-matrix bootstrap for the 2-to-2 S-matrix of gapped theories. To date, this is the only result of this sort, while a contrario no current technology allows to generate, even numerically, fully consistent S-matrices in d>2. Beyond the mathematical results themselves, the proof, based on establishing the existence of a fixed point of a certain map, also suggests a procedure to be implemented numerically and which would produce fully consistent S-matrix functions via iterating dispersion relations, and using as an input a quantity related to the inelasticity of a given scattering process. In this talk, I will report on some work being finalised, done in collaboration with A. Zhiboedov, about analytical and numerical aspects of developing and implementing this scheme. I will review basic concepts of the S-matrix program and show some of our results on non-perturbative scalar, phi^4-like S-matrices in 4, describe their properties and compare to other approaches in the literature. If time allows, I will present some results in 3 dimensions and discuss subtle aspects of the high energy (Regge behaviour) of the S-matrices.

Dynamical Chern-Simons gravity (dCS) is a four-dimensional parity-violating extension of general relativity. Current models predict the effect of this extension to be negligible due to large decay constants f close to the scale of grand unified theories. Here, we present a construction of dCS allowing for much smaller decay constants, ranging from sub-eV to Planck scales. Specifically, we show that if there exists a fermion species with strong self-interactions, the short-wavelength fermion modes form a bound state. This bound state can then undergo dynamical symmetry breaking and the resulting pseudoscalar develops Yukawa interactions with the remaining long-wavelength fermion modes. Due to this new interaction, loop corrections with gravitons then realize a linear coupling between the pseudoscalar and the gravitational Chern-Simons term. The strength of this coupling is set by the Yukawa coupling constant divided by the fermion mass. Therefore, since self-interacting fermions with small masses are ideal, we identify neutrinos as promising candidates. For example, if a neutrino has a mass mν ≲meV and the Yukawa coupling is order unity, the dCS decay constant can be as small as f∼10^3mν ≲eV. We discuss other potential choices for fermions.

The seminar has been cancelled.

We consider graviton scattering in maximal supergravity on Anti-de Sitter space (AdS) in d+1 dimensions for d=3,4,and 6 with no extra compact spacetime factor. Holography suggests that this theory is dual to an exotic maximally supersymmetric conformal field theory (CFT) in d dimensions whose only light single trace operator is the stress tensor. This contrasts with more standard cases like Type IIB string theory on AdS_5x S^5 dual to N=4 Super-Yang-Mills, where the CFT has light single trace operators for each Kaluza-Klein mode on S^5. We compute the 1-loop correction to the pure AdS_{d+1} theory in a small Planck length expansion, which is dual to the large central charge expansion in the CFT. We find that this correction saturates the most general non-perturbative conformal bootstrap bounds on this correlator in the large central charge regime for d=3,4,6. After imposing theory-specific constraints from localization in d=3,4, the bootstrap constraints strengthen and are then saturated by the string/M-theory dual CFT data.

We will review a recent application of Exceptional Field Theory : finding new families of solutions of type IIB supergravity on AdS_4 x S^1 x S^5. To find such solutions, we will compactify type IIB on S^5 x S^1 to obtain a 4d gauged maximal supergravity where new solutions are simply found by extremising a scalar potential. Surprisingly, it is sometime possible to deform our new solutions and break any residual supersymmetry while preserving stability. This is surprising since, from a holographic perspective, these deformations should be dual to non-supersymmetric exactly marginal deformations. We will show that it is a generic behaviour of gravity theories compactified on a circle and we will provide a solution generating technique in terms of a tool called the mapping torus.

In my talk I will review the recent progress in non-local infinite derivative gravity theories. The core of the models under investigation is the infinite derivative generalization of the quadratic gravity theory which was first studied in depth by Stelle in 1977. I will explain why unitarity can only be restored for an infinite tower of derivatives. The rest of the talk will concentrate on the cosmological consequences of this non-local gravity proposal for the Starobinsky inflation.

I will discuss the large N behavior of partition functions of the ABJM theory on compact Euclidean manifolds. I will pay particular attention to the S^3 free energy and the topologically twisted index for which I will present closed form expressions valid to all orders in the large N expansion. These results have important implications for holography and the microscopic entropy counting of AdS_4 black holes which I will discuss. I will also briefly discuss generalizations to other SCFTs arising from M2-branes.

Quantum field theory of higher-spin particles is a formidable subject, where Lorentz-invariant approaches tend to lead to a rich gauge-symmetry structure, which serves to preserve the physical number of degrees of freedom. Introducing consistent interactions in such approaches is a non-trivial task, with most higher-spin Lagrangians specified only up to three points. In this talk, I will discuss a new, chiral description for massive higher-spin particles, which in four spacetime dimensions allows to do away with this kind of gauge symmetry. This greatly facilitates the introduction of consistent interactions. I will concentrate on three theories, in which higher-spin matter is coupled to electrodynamics, non-Abelian gauge theory or gravity. These theories are currently the only examples of consistent interacting field theories with massive higher-spin fields. The presented theories are chiral and have simple Lagrangians, resulting in Feynman rules analogous to those of massive scalars. In particular, I will discuss the resulting tree-level scattering amplitudes with two higher-spin matter particles and any number of positive-helicity photons, gluons or gravitons. These amplitudes were previously computed via on-shell recursion and provided evidence for the existence of such simple massive higher-spin theories.

The fundamental theory of quantum gravity is expected to manifest itself at low energies via a series of higher-derivative corrections to Einstein’s theory. Holography and supersymmetry are of great help to characterize such corrections in controlled scenarios: through holography, quantum gravity in Anti de Sitter (AdS) space has a rigorous definition in terms of a conformal field theory (CFT), while supersymmetry makes it possible to compute exact observables and make quantitative predictions. In this context, we will illustrate how a CFT generating function known as the superconformal index provides a microscopic explanation of the entropy of five-dimensional supersymmetric black holes in AdS. We will show how this match goes beyond the leading Bekenstein-Hawking term and includes higher-derivative corrections.

Matrix theory is a proposed non-perturbative definition of superstring theory in which space is emergent. Recently, it was shown that a 4-dimensional expanding universe can emerge in the IKKT matrix model, with another 6 spatial dimensions stabilized at the string scale. This scenario was also explored in the BFSS model, in which case the emerging phase yields a scale-invariant spectrum of scalar and tensor perturbation. In this talk, we will discuss recent progress in understanding these results. More precisely, we will discuss a possible way of obtaining the metric out of the matrices in the IKKT model, and ways to probe symmetry breaking in the BFSS model.

Second order thermal phase transitions are driven my an order parameter which comes with an amplitude. Fluctuations of this amplitude lead to a slowly decaying mode whose gap closes to zero at the critical point. I will use holographic techniques to discuss in detail how this gapped mode determines the linear response of scalar operators close to the phase transition and give a geometric expression for the dissipative coefficient that fixes the relevant Green’s functions.

In recent years, it has been understood how local operators do not paint the entire picture of a quantum field theory, but we need to introduce extended operators to understand finer details about these theories. Motivated by this, we investigate a subset of these extended operators in particular in the context of 4d N=2 superconformal field theories. I will start by introducing the setup that we use to describe the possible configurations of these extended operators. I will also compare and contrast the operators that appear in our framework with the more familiar (Wilson and 't Hooft) line operators. Time permitting, I will then introduce twists of these theories by a choice of an appropriate nilpotent supercharge. The restriction to (extended) operators living in the cohomology of this supercharge gives rise to interesting algebraic structures, that are analogous to, or rather an extension of, the 2d vertex operator algebras that have now become familiar familiar in the context of 4d N=2 theories.

In this talk we will introduce CosmoLattice, a modern code for simulating the non-linear dynamics of interactive scalar-gauge theories in an expanding universe. As a demonstration of its power we will solve three very different problems of early Universe cosmology: i) the generation and use of gravitational waves as a probe of particle couplings, ii) the dynamics of non-minimally coupled scalar fields in the Jordan frame, and iii) the non-linear dynamics of helical gauge field production during the last efoldings of axion-inflation