String Seminar Archive: 2022-2023

Very compact stars seem to be forbidden in General Relativity. While Buchdahl's theorem sets an upper bound on compactness, further no-go results rely on the existence of two light rings, the inner of which is associated to gravitational instabilities. However, little is known about the role of QFT in these strong gravity regimes. We show that the renormalized stress tensor for CFTs diverges faster than the classical source as the star's surface approaches the Buchdahl radius rather than the Schwarzschild radius. The backreaction of quantum fields in this regime therefore cannot be ignored. Based on 2301.00826 with G. Tomaselli.

Determining the phase structure of Quantum Chromodynamics (QCD) and its Equation of State (EoS) at densities and temperatures realised inside neutron stars and their mergers is a long-standing open problem. I will present a framework for the EoS of dense and hot QCD that describes the deconfinement phase transition between a dense baryonic and quark matter phase via the holographic V-QCD model. This model is then used in fully general relativistic hydrodynamic simulations of binary systems that are consistent with the first ever observed neutron star merger event GW170817 and the consequences on the formation of quark matter and the emitted gravitational wave signal are studied.

Despite its apparent simplicity, the conformal Carrollian scalar field admits an infinite number of higher symmetries. In this talk, we show that a restriction of the symmetry algebra is identical to a recently proposed symmetry algebra for higher-spin fields in Minkowski spacetime. This higher-spin algebra also admits an extension of the type of BMS, thus constituting an interesting candidate for a higher-spin asymptotic symmetry algebra. The conformal Carrollian scalar is thus a natural candidate to study higher-spin symmetries in flat spacetime form a holographic perspective, similarly to what happens in higher-spin AdS/CFT.

The experimental absence of low-energy supersymmetry, together with theoretical swampland arguments, leave the door open for high-energy supersymmetry breaking. Non-supersymmetric string theory provides such an arena, and it is important to investigate its consistency with swampland principles. I will present some of the first results in this direction, discussing brane dynamics in simple flux vacua. A number of swampland criteria hold: de Sitter vacua are obstructed, gravity is the weakest force and (suitably generalized) infinite-distance limits in the space of vacua behave according to the emergent string conjecture, possibly hinting at a mysterious novel realization of S-duality. To wit, at the edges of the space of vacua either extra dimensions decompactify or a unique (D-)string becomes tensionless, and both phenomena occur exponentially fast in terms of a properly defined measure of distance.

Despite the conventional reasonings, the naive expectation of ​​canonically quantizing all down within physical spacetime seems erroneous. This would, of course, imply a drastic shift in our understanding of what is often referred to as quantum gravity. I assert that such a picture is what quantum black holes and the holographic principle indeed suggest. In this seminar talk, I will motivate and recapitulate the resulting proposal, and detail out the underlying arguments, as recently presented in arXiv:2208.01019.

We study the vacua of 4d heterotic toroidal orbifolds using effective theories consisting of an overall Kähler modulus, the dilaton, and non-perturbative corrections to both the superpotential and Kähler potential that respect modular invariance. We prove three de Sitter no-go theorems for several classes of vacua and thereby substantiate and extend previous conjectures. Additionally, we provide evidence that extrema of the scalar potential can occur inside the PSL(2,Z) fundamental domain of the Kähler modulus, in contradiction of a separate conjecture. We also illustrate a loophole in the no-go theorems and determine criteria that allow for metastable de Sitter vacua. Finally, we identify inherently stringy non-perturbative effects in the dilaton sector that could exploit this loophole and potentially realize de Sitter vacua. 

Quantum backreaction in semi-classical gravity is a  notoriously difficult task. In this talk, I will explain how braneworld holography can help us tackle this problem. I will review some basic properties of braneworld models with or without a cosmological constant, emphasizing various semi-classical properties of the solutions. As an application, I will consider the backreaction due to conformal matter in conical de Sitter space and show that it gives rise to quantum dS black holes in 3D, solutions that do not have a classical counterpart. Time permitting, I will also show some results on entanglement islands in de Sitter space, and how to recover a unitary Page curve from the braneworld perspective. The discussion will be based on arXiv:2207.03302 and work in progress.

Gauge-gravity duality plays a key role in understanding quantum gravity and strongly interacting gauge theories, however, lacks a satisfactory microscopic derivation. Fundamental questions such as, how does gravity emerge directly from quantum field theory observables and how to determine which QFTs are holographic, which are not, remain unanswered. In this talk, I propose a primitive form of gauge-string duality based on the worldline formulation of perturbative QFT. In particular we consider L loop quantum corrections to correlation functions in an holographic QFT where a Schwinger parameter is associated to each internal propagator in the corresponding Feynman diagrams. We argue that embedding of the holographic coordinate in string theory emerges from the collection of these Schwinger parameters in the continuum limit of the Feynman diagrams. As a by product, we provide a novel Kallen-Lehmann representation of two-point functions as a sum over boundary-to-boundary propagators of massive bulk scalars in AdSd+1 with masses determined by L. This novel approach can be generalized to arbitrary N. Therefore it might have two potential uses: to provide  i) a non-perturbative approach to quantum gravity in terms of perturbative QFT at finite N, ii) a true bottom-up holographic construction for confining gauge theories like QCD derived directly from QCD amplitudes.

I will discuss a counterexample to the CFT convexity conjecture, a conjecture about the convexity of the minimal operator dimension as a function of Q (call it Delta[Q]) in generic CFTs with (only one) U(1) global symmetry 2108.04594. The conjecture states that the function Delta[n*Q_0] is a convex function of n for any Q_0 larger than some O(1) number, for any CFTs of this type. It was naturally motivated by a version of the Weak Gravity Conjecture, called the Positive Binding Energy conjecture 1705.04328. By incorporating a clock-work like mechanism to construct a weakly-coupled but nevertheless interacting CFT with only one U(1) symmetry, we show that such a statement is not true in general. The talk will be based on 2301.08262.

Positive scalar potentials in string effective theories could provide an origin to Dark Energy, responsible for the accelerated expansion of our universe today or during inflation. It is thus crucial to characterise these scalar potentials, namely their slope, their critical points (de Sitter solutions) and the associated stability, as also advocated by the Swampland Program. We will present such characterisations. Going further, we will also discuss negative scalar potentials, and make related observations on anti-de Sitter solutions, in particular on a new mass bound, as well as comments on scale separation.

The Planck scale serves as a fundamental UV cut-off in gravitational theories, however, when light species are present a lower scale called the species scale plays that role. In this talk we will discuss recent work on this species scale from two directions. From the top-down we propose and explore a definition of the species scale in Type II Calabi-Yau compactifications that is valid everywhere in moduli space. From the bottom-up we argue for an upper bound on the gradient of this species scale, which remarkably is saturated by the exponential behavior in the distance conjecture.

Within the AdS/CFT correspondence, the entanglement properties of the CFT are related to wormholes in the dual gravity theory. This gives rise to questions about the factorisation properties of the Hilbert spaces on both sides of the correspondence.  We  show how the Berry phase, a geometrical phase encoding information about topology, may be used to reveal similarities between the Hilbert space structure on both sides of the correspondence. Mathematical concepts such as coadjoint orbits play an important role. Moreover, there is a relation to the von Neumann algebras recently studied in the context of AdS/CFT. In addition to its relevance for quantum gravity, this analysis also suggests how to experimentally realise the Berry phase and its relation to entanglement in table-top experiments involving photons or electrons. This provides a new example for relations between very different branches of physics that follow from the AdS/CFT correspondence and its generalisations.

Based on 2109.06190, 2202.11717 and work in progress. (Links open in a new window/tab)

In this talk, I will discuss the motivation for considering an extra mesoscopic `Dark Dimension' of length $l \sim \Lambda^{-1/4} \sim 10^{-6}\;\mathrm{m}$, taking into account theoretical and observational arguments. I will then talk about cosmological aspects of the Dark Dimension. In particular this scenario leads, by the universal coupling of the Standard Model sector to bulk gravitons, to massive spin 2 KK excitations of the graviton in the Dark Dimension (the “dark gravitons”) as an unavoidable dark matter candidate. This model can also provide a new perspective on the cosmological coincidence problem, where the matter/radiation equality temperature ($T \sim 1\;\mathrm{eV}$) is close to the temperature where the dark energy begins to dominate. Thus, one does not need to appeal to Weinberg’s anthropic argument to explain this coincidence. The dark gravitons are produced at $T_i \sim 1\;\mathrm{GeV}$, and their composition changes as they mainly decay to lighter gravitons, without losing much total mass density. The mass of dark gravitons is $m_\mathrm{DM}\sim 10 - 100\;\mathrm{keV}$ today. These features of the Dark Dimension scenario distinguish its cosmology from the standard $\Lambda$CDM model. In particular, the decay of dark gravitons imparts non-zero velocity to DM particles leading to less structure. Given the $S_8$ tension in cosmology, this leads to a mild $\sim 3 \sigma$ preference for the Dark Dimension scenario compared to $\Lambda$CDM.

In general, a projective Calabi-Yau threefold with nodal signularities does not admit a Kaehler small resolution. This happens in particular if the exceptional curves are torsion in homology. In this talk we will discuss how the classical relationship between topological string theory, enumerative geometry and mirror symmetry generalizes to this setting. After recalling some of the ideas from the smooth case, we will both explain the physical intuition behind the generalization and translate it into an concrete mathematical proposal. At the end of the talk, if time permits, we will highlight some open questions that follow from this proposal, related to Donaldson-Thomas theory, non-commutative geometry, and FJRW-theory. 

In this talk we introduce particular TQFTs in three dimensions, known as Symmetry Topological Field Theories (or SymTFTs), to identify line defects of two-dimensional CFTs arising from the compactification of 6d (2,0) SCFTs on 4-manifolds M4. The mapping class group of M4 and the automorphism group of the SymTFT switch between different absolute 2d theories or global variants. Using the combined symmetries, we realize the topological defects in these global variants. Our main example is P1 x P1. For N M5-branes the corresponding 2d theory inherits ZN 0-form symmetries from the SymTFT. Moreover, we find duality defects at fixed points of the coupling constant under elements of the mapping class group which together with the ZN symmetries form a TY[ZN] fusion category. We also comment on other Hirzebruch surfaces, del Pezzo surfaces, as well as the connected sum of P1 x P1. 

We analyze infinite-distance limits in the complex structure moduli space of six-dimensional F-theory, giving an algebro-geometric classification and a physical interpretation. From the point of view of the Swampland Program, the motivation is to understand the fate of open-moduli infinite-distance limits in relation with the Distance Conjecture. From an F-theory perspective, the infinite-distance limits correspond to suitable non-minimal singularities in codimension one and higher. While codimension-two finite-distance non-minimal singularities have been understood as SCFTs in a major classification effort, the goal of our analysis is to elucidate the meaning of the infinite-distance codimension-one and codimension-two non-minimal singularities. We argue why the limits over P^1-fibered bases are a natural starting point for the detailed analysis, and comment on our results showing that they are either decompactification limits or emergent string limits in a dual sense.

We study the relationship between shockwave geometries and the gravitational memory effect in four-dimensional asymptotically flat spacetime. In particular, we show the 't Hooft commutation relations of shockwave operators are equivalent to the commutation relation between soft and Goldstone modes parametrizing a sector of the gravitational phase space. We demonstrate this equivalence via a diffeomorphism that takes the shockwave metric to a metric whose transverse traceless component is the gravitational memory. The shockwave momentum in 't Hooft's analysis is related to the soft graviton mode, which is responsible for the memory effect, while the shift in the shockwave position is related to the Goldstone mode. This equivalence opens new directions to utilize the gravitational memory effect to explore the observational implications of shockwave geometries in flat space.

We explicitly construct the quantum field theory corresponding to a general class of deep neural networks encompassing both recurrent and feedforward architectures. We first consider the mean-field theory (MFT) obtained as the leading saddlepoint in the action, and derive the condition for criticality via the largest Lyapunov exponent. We then compute the loop corrections to the correlation function in a perturbative expansion in the ratio of depth T to width N, and find a precise analogy with the well-studied O(N) vector model, in which the variance of the weight initializations plays the role of the 't Hooft coupling. In particular, we compute both the O(1) corrections quantifying fluctuations from typicality in the ensemble of networks, and the subleading O(T/N) corrections due to finite-width effects. These provide corrections to the correlation length that controls the depth to which information can propagate through the network, and thereby sets the scale at which such networks are trainable by gradient descent. Our analysis provides a first-principles approach to the rapidly emerging NN-QFT correspondence, and opens several interesting avenues to the study of criticality in deep neural networks.)

Infinite distance limits have been observed to enjoy a number of universal properties: they have "logarithmic" metric singularities, are always associated with weak-coupling limits, and are associated with the appearance of a tower of exponentially light fields as described by the Swampland Distance Conjecture. Using information theory, I will explain how the first two of these universal features are a consequence of unitarity, which dictates that infinite distance limits always correspond to limits in which observables factorize and enforces a logarithmic metric singularity. I will also explain why such limits necessarily have dramatic quantum gravitational behavior. Gravity couples universally to stress-energy and obstructs factorization limits. Gravity must then decouple in consistent factorization limits. I will explain how this both provides a bottom-up motivation for the Swampland Distance Conjecture and points towards ways around it.

We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the time-dependent evolution operator and the origin within the group of unitaries. (An appropriate `complexity metric' must be used that takes into account the relative difficulty of performing `nonlocal' operations that act on many degrees of freedom at once.) While simply formulated and geometrically attractive, this notion of complexity is numerically intractable save for toy models with Hilbert spaces of very low dimensions. To bypass this difficulty, we trade the exact definition in terms of geodesics for an upper bound on complexity, obtained by minimizing the distance over an explicitly prescribed infinite set of curves, rather than over all possible curves. Identifying this upper bound turns out equivalent to the closest vector problem (CVP) previously studied in integer optimization theory, in particular, in relation to lattice-based cryptography. Effective approximate algorithms are hence provided by the existing mathematical considerations, and they can be utilized in our analysis of the upper bounds on quantum evolution complexity. The resulting algorithmically implemented complexity bound systematically assigns lower values to integrable than to chaotic systems, as we demonstrate by explicit numerical work for Hilbert spaces of dimensions up to ~10^4.)

This talk will start with an introduction to hydrodynamisation in an FRW universe. I first briefly describe the set-up and show how a hydrodynamic plasma dilutes and falls out of equilibrium due to expansion towards empty de Sitter spacetime [1]. Next, I will show new technical advances that allowed us to dynamically evolve the boundary metric in accordance with the Friedmann equations [2]. Previously unphysical renormalisation constants now become physical parameters and depending on the boundary cosmological constant this leads to de Sitter, asymptotically flat or Big Crunch cosmologies. Time permitting I will show some new results where we have a rolling inflation on the boundary that heats up the boundary QFT.

1. Jorge Casalderrey-Solana, Christian Ecker, David Mateos and WS, Strong-coupling dynamics and entanglement in de Sitter space, 2011.08194 (SciPost Phys)
2. Christian Ecker, WS, David Mateos and Jorge Casalderrey-Solana, Holographic Evolution with Dynamical Boundary Gravity, 2109.10355 (JHEP)

The smallness of the cosmological constant Λ, together with swampland ideas, lead to the recent Dark Dimension proposal, which postulates that there exists a single mesoscopic extra dimension with size of a few micrometers. In particular, a single tower of light states should appear, with masses scaling like m ~ Λ^{1/4}. In this talk, I will review how the Dark Dimension proposal arises and some of its main implications. I will explain how a strongly warped throat with its redshifted KK tower provides a natural string-theoretical mechanism realizing the required scaling, with the dark dimension being the one along the throat. I will point out challenges that may arise when considering such a setup, in particular concerning the masses of other KK towers.

In large-𝑁 gauge theories, evidence has emerged recently that between confined and deconfined phases a partially-deconfined phase can appear, in which only a subset of colours deconfine. The existence of such a phase has implications for the map between degrees of freedom under gauge/gravity duality and black hole phase diagrams, where a counterpart to the partially-deconfined saddle should be present. We investigate properties of partial deconfinement on the field theory side, first considering the partially-deconfined saddle of large-𝑁 pure Yang-Mills theory. Here, the colour degrees of freedom split into confined and deconfined sectors. We argue with the use of numerical simulations that a linear confinement potential is generated in the confined sector, implying the formation of flux tubes, whereas the potential is screened in the deconfined sector and behaves instead according to the perimeter law. Furthermore, we find that the onset of partial deconfinement coincides with the breaking of chiral symmetry, providing an order parameter for the partially-deconfined phase. We conjecture that global symmetries can be used to signify partial deconfinement, leading also to an associated order parameter. As another, cleaner example of this, we show that CP symmetry breaking coincides precisely with the emergence of the partially-deconfined phase in supersymmetry-broken N=1 super-Yang-Mills with a theta-angle 𝜃=𝜋, for both large finite 𝑁 and the formal large-𝑁 limit. Finally, we discuss consequences of these findings for holography and the QCD crossover.