Bootstrap methods have greatly expanded our ability to compute correlation functions in the supergravity approximation. As a result, we now know Mellin space expressions for general half-BPS four-point functions at tree-level in the main holographic CFTs with maximal supersymmetry. These are the $\mathcal{N} = (2,0)$ theory in six dimensions, $\mathcal{N} = 4$ Super Yang Mills in four dimensions and $\mathcal{N} = 8$ ABJM theory in three dimensions. In all three cases, a rich subsector of operators that generate an infinite dimensional symmetry may be constructed by passing to the cohomology of a certain nilpotent supercharge. I will explain the main features of this construction and how they may be accessed holographically. When the protected operators generate a W-algebra, we will see that their four-point functions agree precisely with those predicted by AdS / CFT thus giving a complete check. The other possibility leads us to consider topological quantum mechanics where the calculations are more difficult. Nevertheless, I will show that an infinite family of special OPE coefficients obeys non-perturbative relations that follow from the one-dimensional theory. https://zoom.us/j/96173937792?pwd=dHNkVVp0T0RtSitFZ2xaUkhqS1VjQT09

I will motivate the possibility that particle Dark Matter (DM) is heavier than the so-called `unitarity limit', of about 100 TeV, and review the proposals to evade it. Among these proposals, I will focus on recent results on supercooled confining phase transitions in the early universe, whose implications are relevant beyond the DM problem. I will finally discuss how these scenarios will be probed at telescopes, underground labs, colliders and gravitational waves detectors. [please email a.held@imperial.ac.uk for zoom link or password]

In holography, the geometry of gravitational theory should be encoded in its non-gravitational dual. In particular, in gauge/gravity duality, the geometry should be encoded into the color degrees of freedom (matrices) in U(N) supersymmetric Yang-Mills theory. When the Yang-Mills theory is regarded as the low-energy effective theory of a system of N D-branes and open strings between them. Transverse spatial directions emerge from scalar fields, which are N*N matrices with color indices; roughly speaking, the eigenvalues are the locations of D-branes. In the past, it was argued that this simple 'emergent space' picture cannot be used in the context of gauge/gravity duality, because the ground-state wave function delocalizes at large N, leading to a conflict with the locality in the bulk geometry. We show that this conventional wisdom is not correct: the ground-state wave function does not delocalize, and there is no conflict with the locality of the bulk geometry. This conclusion is obtained by clarifying the meaning of the 'diagonalization of a matrix' in Yang-Mills theory, which is not as obvious as one might think. This observation opens up the prospect of characterizing the bulk geometry via the color degrees of freedom in Yang-Mills theory, all the way down to the center of the bulk. [please email a.held@imperial.ac.uk for zoom link or password]

In type II strings compactified on a Calabi-Yau threefold $X$, the Donaldson-Thomas (DT) invariants $\Omega(\gamma,z)$ counting BPS black holes have an intricate dependence on the moduli $z$, due to wall-crossing phenomena. When $X$ is a toric threefold, these indices are related to the DT invariants of a quiver with potential with superpotential, encoded by a brane tiling. I will present a conjecture for the DT invariants for all dimension vectors $d$ in a certain chamber $z_*(d)$ known as the attractor (or self-stability) chamber. In short, "DT invariants all vanish, except when they are known not to." In combination with the attractor flow tree formulae, this conjecture provides an algorithmic way of computing the DT invariants $\Omega(\gamma,z)$ for any $\gamma,z$. The conjecture is supported by a large number of checks, including a successful comparison with the Vafa-Witten invariants of a Fano surface $S$ when $X$ is the total space of the canonical bundle $K_S$, and with the counting of molten crystals for framed DT invariants in the non-commutative chamber. Based on works with G. Beaujard, J. Manschot and S. Mozgovoy, arXiv:2004.14466 and 2012.14358 Join Zoom Meeting https://zoom.us/j/94029175955?pwd=b1hvVnVxbFZjTmM5bkxaWi93VkpzUT09 Meeting ID: 940 2917 5955 Passcode: 086150

Analytical models of structure formation are an important tool, complementary to N-body simulations, to investigate the formation of cosmic structures and the dependence of their statistics on cosmological parameters. They rely on some non-linear map, typically spherical collapse, to relate topological features of the initial density field (number of maxima, minima, saddles, critical points...) to different types of structures and events (halos, voids, filaments, mergers...) in the cosmic web. I will give a broad introduction to the topic and discuss some recent developments. [please email a.held@imperial.ac.uk for zoom link or password]

We will discuss the relation between primordial black holes and gravitational waves in the view of the recent Ligo/Virgo and NanoGrav data. [please email a.held@imperial.ac.uk for zoom link or password]

The first talk will be general, i.e., at a colloquium level. The second talk will be more technical, i.e., at a seminar level. Yet, each of the two talks will be self-contained. For this reason, there will be some overlap between them. Talk 1: Quantum Field Theory and Beyond We will review the status of Quantum Field Theory (QFT) and will present it as “the language of physics.” Using examples from string theory and condensed matter physics, we will motivate the fact that the standard framework of QFT should be extended. As specific examples, we will review the phenomena of fractons, which do not seem to fit the standard framework of continuum QFT. We will then present recent attempts to incorporate fractons in a slightly generalized version of quantum field theory. Talk 2: Fractons: going beyond standard QFT Starting with a lattice system at short distances, its long-distance behavior is captured by a continuum Quantum Field Theory (QFT). This description is universal, i.e., it is independent of most of the details of the microscopic system. Surprisingly, certain recently discovered lattice systems, and in particular models of fractons, seem to violate this general dogma. Motivated by this apparent contradiction, we will present exotic continuum QFTs that describe these systems.

Gravitational waves are expected to be an important probe of physics beyond the Standard Model, through their production at first order phase transitions. I will report on recent work on characterising the gravitational wave power spectrum, and outline some BSM physics which might be probed at the future space-based gravitational wave detector LISA. [please email a.held@imperial.ac.uk for zoom link or password]

We investigate emergent gravity extending the paradigm of the AdS/CFT correspondence. The emergent graviton is associated to the (dynamical) expectation value of the energy-momentum tensor. We derive the general effective description of such dynamics, and apply it to the case where a hidden theory generates gravity that is coupled to the Standard Model. In the linearized description, generically, such gravity is massive with the presence of an extra scalar degree of freedom. The propagators of both the spin-two and spin-zero modes are positive and well defined. The associated emergent gravitational theory is a bi-gravity theory, as is (secretly) the case in holography. The background metric on which the QFTs are defined, plays the role of dark energy and the emergent theory has always as a solution the original background metric. In the case where the hidden theory is holographic, the overall description yields a higher-dimensional bulk theory coupled to a brane. The effective graviton on the brane has four-dimensional characteristics both in the UV and IR and is always massive. [please email a.held@imperial.ac.uk for zoom link or password]

We study the N = 4 SU(N) super-Yang-Mills stress tensor multiplet four-point function at large N and finite complexified Yang-Mills coupling tau, which is dual to the Type IIB graviton correlator on AdS_5 × S^5 at large string length and finite string coupling. The specific four-point functions we consider are integrated correlators obtained by taking various combinations of four derivatives of m, b, and tau of the sphere free energy deformed by mass m and squashing parameter b, which can be computed using supersymmetric localization. We show that at each order in 1/N, these quantities can be written in terms of modular invariants, such as the well studied non-Holomorphic Eisenstein series as well as some new generalizations thereof. These results reproduce known features of the low-energy expansion of the four-graviton amplitude in type IIB superstring theory in ten-dimensional flat space, which is the first check of AdS/CFT at finite string coupling, and have interesting implications for the structure of the analogous expansion in AdS_5 × S^5. Zoom Join Zoom Meeting https://zoom.us/j/93725965823?pwd=Q2lmeEhjQnJmZUsxMkp2THdVZ1cxUT09 Meeting ID: 937 2596 5823 Passcode: 640955

AdS/CFT provides a consistent non-perturbative definition of quantum gravity in asymptotically AdS spacetimes. Black holes correspond to ensembles of states in the boundary field theory. In the presence of supersymmetry, we rephrase the problem of counting those states in terms of a supersymmetric partition function: the superconformal index. By performing a careful analysis of the index of 4d N=4 SU(N) Super-Yang-Mills theory, with the help of a Bethe Ansatz approach, we are able to exactly reproduce the Bekenstein-Hawking entropy of BPS black holes in AdS5 x S5. The large N limit exhibits many competing contributions, that we are able to identify with complex saddles of the (putative) gravitational path-integral. Along the way we propose a necessary condition for complex saddles to contribute, based on the size of their non-perturbative corrections.

We are faced with an explosion of data in many areas of physics, but very so often, it is not the size but the complexity of the data that makes extracting physics from big datasets challenging. As I will discuss in this talk, data has shape and the shape of data encodes the underlying physics. Persistent homology is a tool in computational topology developed for quantifying the shape of data. I will discuss three applications of topological data analysis: 1) identifying structure of the string landscape, 2) constraining primordial non-Gaussianity from CMB measurements and large scale structures data, and 3) detecting and classifying phases of matter. Persistent homology condenses these datasets into their most relevant (and interpretable) features, so that simple statistical pipelines are sufficient in these contexts. This suggests that TDA can be used in conjunction with machine learning algorithms and improves their architecture. Based on https://arxiv.org/abs/2009.14231, https://arxiv.org/abs/2009.04819, https://arxiv.org/abs/1907.10072, https://arxiv.org/abs/1812.06960, https://arxiv.org/abs/1712.08159. [please email a.held@imperial.ac.uk for zoom link or password]

The most famous slogan of the Swampland program is that not all effective field theories (EFTs) admit ultraviolet completion into quantum gravity. In this talk, we focus on the significance of this claim for EFTs which involve scalar field variations and on the implications for cosmology. To conclude, we examine some concrete string-phenomenological set-ups with warped throats. [please email a.held@imperial.ac.uk for zoom link or password]

``We explore the construction and stability of asymptotically anti-de Sitter Euclidean wormholes in a variety of models. In simple ad hoc low-energy models, it is not hard to construct two-boundary Euclidean wormholes that dominate over disconnected solutions and which are stable (lacking negative modes) in the usual sense of Euclidean quantum gravity. Indeed, the structure of such solutions turns out to strongly resemble that of the Hawking-Page phase transition for AdS-Schwarzschild black holes, in that for boundary sources above some threshold we find both a `large' and a `small' branch of wormhole solutions with the latter being stable and dominating over the disconnected solution for large enough sources. We are also able to construct two-boundary Euclidean wormholes in a variety of string compactifications with a similar that dominate over the disconnected solutions we find and that are stable with respect to field-theoretic perturbations. However, as in classic examples investigated by Maldacena and Maoz, the wormholes in these UV-complete settings always suffer from brane-nucleation instabilities (even when sources that one might hope would stabilize such instabilities are tuned to large values). This indicates the existence of additional disconnected solutions with lower action. We discuss the significance of such results for the factorization problem of AdS/CFT.’' Join Zoom Meeting https://zoom.us/j/98062076339?pwd=aGJNUTBTNjBYeDhqUlZVMzdVWkhGQT09 Meeting ID: 980 6207 6339 Passcode: 913115

The search for extensions to GR, has prompted the developments of many potential options which, to varying degrees, have been studied and confronted with observations in special regimes --typically linear ones with respect to rather 'simple' scenarios. Gravitational wave astronomy provides the opportunity to confront them in a much richer and complex regime which unearths significant roadblocks that obstruct the definition and/or study of consequences of many of such extensions. This talk will review some of these problems, illustrate consequences and discuss a potential way through for studying the potential role such extensions might have in the strongly gravitating/non-linear regime. [please email a.held@imperial.ac.uk for zoom link or password]

Cosmic strings arise as remnants of phase transitions in the early Universe, often related to theories of grand unification (GUTs). If such a phase transitions occurs at high energies, the resulting cosmic string network generates a sizable amount of gravitational waves. Most work so far has focused on the gravitational wave signal from topologically stable cosmic strings. In this talk I will introduce metastable cosmic strings, which are a generic consequence of many GUTs. I will discuss how this idea can be probed in various ongoing and upcoming gravitational wave experiments, from pulsar timing arrays to space- and ground-based interferometers. In the final part of my talk I will discuss a recent proposal on using the radio telescopes to probe this and other sources of ultra high frequency gravitational waves. [please email a.held@imperial.ac.uk for zoom link or password]

I will perform a consistent reduction of 6d matter-coupled F(4) gauged supergravity on a compact Riemann surface of genus g, at the level of the bosonic fields. The result is an N=2 gauged supergravity coupled to two vector multiplets and a single hypermultiplet. The four-dimensional model is holographically dual to the 3d superconformal field theories of class F, describing different brane systems in massive type IIA and IIB wrapped on the Riemann Surface. I will then use the results to find the first examples of dyonic static black holes of class F and perform a microscopic counting of their entropy via the 5d topologically twisted index. I will also find new asymptotically AdS solutions, including rotating black holes, in the subtruncations of the 4d model, providing predictions for the squashed S^3 partition functions and the superconformal and refined twisted indices of class F field theories. Join Zoom Meeting https://zoom.us/j/92805841030?pwd=dTVGQ2h5ZUw4cndKd3JUYTNYVTMrdz09 Meeting ID: 928 0584 1030 Passcode: 902526

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The n-point tachyon amplitude is a classic and well-known result in bosonic string theory. Rather than studying tachyon amplitudes, we will compute scattering amplitudes involving highly excited string states. Along the way we review and elaborate on the DDF construction of string vertex operators, and describe properties of a generic excited string. Based on work in progress with D. Gross.

Recently, theories with higher rank gauge symmetries are drawing attention in condensed matter physics. Such theories are thought to be related to the so-called "fractons," quasiparticles with limited mobility that appear in some lattice models. We show that one version of such higher ranked symmetry can be "nonlinearlized" into volume-preserving diffeomorphism. We demonstrate that several condensed matter systems, including the fractional quantum Hall effect and ferromagnetism, secretly possess this symmetry, which sheds another light to some peculiar features of the quasiparticles in these systems. [please email a.held@imperial.ac.uk for zoom link or password]