The standard formulation of General Relativity is based on a geometrical framework where the spacetime manifold is endowed with a Lorentzian metric and its associated Levi-Civita connection. Since the affine structure is independent of the metric, it is possible to extend this geometrical set-up to allow for more general connections, thus giving rise to the metric-affine framework where the new actors are the torsion and the non-metricity. After discussing how these two objects can provide equivalent descriptions of GR, I will discuss how pathologies arise in modified theories of gravity along different directions in the metric-affine landscape. [please email a.held@imperial.ac.uk for zoom link or password]

Does our world respect causality at all energy scales? We explore constraints on low-energy dynamics which step from this assumption. Obstructions to a causal UV completion can be diagnosed using dispersive sum rules, which connect the infrared and ultraviolet. While dispersion relations originate in optics and quantum field theory, I will argue that their true purpose is gravity, where they become particularly powerful due to the maximal growth rate of this force with energy. This leads to the so-called graviton pole in sum rules. I will briefly review how, for non-gravitational low-energy effective theories, causality turns dimensional analysis estimates into sharp numerical bounds, and I will present initial results on gravitational effective theories. [please email a.held@imperial.ac.uk for zoom link or password]

I will start by introducing the two fundamental pillars of Cosmology: General Relativity and the Cosmological Principle. General Relativity will be constructed both in the geometrical as well as in the particle physics perspective. After introducing some of the prominent effective field theories of gravity I will show how the Cosmological Principle can be realized in the different theories. I will then discuss how different theoretical consistency checks can be applied on them for their scrutiny, like conditions coming from a UV completion and quantum corrections. I will argue that we will need to combine this theoretical scrutiny program with different cosmological observations in order to disentangle between different dark energy models and test fundamental properties of gravity. [please email a.held@imperial.ac.uk for zoom link or password]

I review new tools for the computation of Kaluza-Klein mass spectra associated with compactifications around various background geometries relevant for string theory. This includes geometries with little to no remaining symmetries, hardly accessible to standard methods. The new tools build on exceptional field theory, the duality covariant formulation of supergravity. Among the applications I discuss the stability of several non-supersymmetric AdS4 and AdS3 vacua, as well as Kaluza-Klein spectra around type IIB S-fold backgrounds. Zoom: https://zoom.us/j/98264204601?pwd=Z0xYdG1vVlEwU1M1bDhVcXQvWURPQT09 Meeting ID: 982 6420 4601 Passcode: 196883

We will review our current understanding of reheating after inflation, including various aspects of the linear and nonlinear dynamics of the inflaton field, such as parametric resonance, the generation of metric perturbations and the effects of the nonlinear evolution on the post-inflationary expansion history. We will also review the recent progress in the understanding of the non-perturbative dynamics of dark vector fields during reheating and whether they can play the role of dark matter in the late universe. Finally, we will discuss phenomenologically interesting models of gauge fields during inflation which can give rise to detectable gravitational wave signatures. [please email a.held@imperial.ac.uk for zoom link or password]

(please note that the time of this semiar has been moved to 15:30)

Everyone seems to have strong opinions these days about what UV completions to gravity can tell us about lower-energy physics. Perceived difficulties finding inflationary solutions to string theory in particular have prompted re-examination of the utility of EFT methods, such as through the swampland trans-Planckian conjectures. This talk provides a curmudgeonly assessment of some of these proposals together with my own opinion about the likely low-energy take-aways of attempts to embed cosmology into string theory. If there is time I will describe some aspects of gravitation EFTs that really do seem to deviate from the standard Wilsonian picture. [please note the unusual time] [please email a.held@imperial.ac.uk for zoom link or password]

Significant progress has been made regarding the microstate counting of extremal AdS black holes in the context of AdS/CFT, where the Cardy-like limit on the field side theory has often been used. I will discuss the implications of this limit on the gravity side and how it translates to a parameter space limit on the black hole solution. This limit, referred to as the gravitational Cardy limit, is applied to the Bardeen Horowitz near-horizon geometry to reproduce the Bekenstein-Hawking entropy via the Kerr/CFT correspondence, yielding a third approach to the computation of the entropy. Relaxing the gravitational Cardy limit, the computation can be further extended to near-extremality, where the heat capacity is found. For each case, extremal and near-extremal, the entropy from these different approaches match, providing a unique and universal expression for the entropy. https://zoom.us/j/98264204601?pwd=Z0xYdG1vVlEwU1M1bDhVcXQvWURPQT09

We will motivate and introduce the study of conformal defects in superconformal field theories (SCFTs). We will show how symmetries constrain the anomaly coefficients of BPS defects. In the case of N=(2,2) surface defects in four-dimensional N=2 SCFTs these anomaly coefficients can be computed by studying a protected sub-sector captured by a two-dimensional chiral algebra. [please email a.held@imperial.ac.uk for zoom link or password]

Motivated by the desire to understand the dynamics of light modes on various gravitational backgrounds, this talk summarizes recent results concerning properties of scalar, vector, and tensor excitations of black holes and integrable stringy geometries. For rotating black holes and for certain Wess-Zumino-Witten models, full separability of all dynamical equations is demonstrated, and symmetries underlying this property are uncovered. For other classes of integrable backgrounds, the energy spectra of various fields are evaluated, and the algebraic constructions of the corresponding eigenfunctions are presented. Join Zoom Meeting https://zoom.us/j/94137164225?pwd=ZTV3Z2c3aStOdk5sSFRRbkhQRUh5dz09 Meeting ID: 941 3716 4225 Passcode: 500873

The NANOGrav Collaboration has recently reported strong evidence for a stochastic common-spectrum process, which we interpret as a SGWB in the framework of cosmic strings. The possible NANOGrav signal would correspond to a string tension Gμ∈(4×10^{−11},10^{−10}) at the 68% confidence level, with a different frequency dependence from supermassive black hole mergers. The SGWB produced by cosmic strings with such values of Gμ would be beyond the reach of LIGO, but could be measured by other planned and proposed detectors such as SKA, LISA, TianQin, AION-1km, AEDGE, Einstein Telescope and Cosmic Explorer. If this interpretation is confirmed future GW measurements would also allow us to probe the expansion history of the Universe to times much before what we can infer from the currently known data. [please email a.held@imperial.ac.uk for zoom link or password]

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]