BPS quivers of five-dimensional SCFTs, Topological Strings and q-Painlevé equations

Five-dimensional SCFTs arise from the low-energy dynamics of M-theory compactified on local (toric) Calabi-Yau threefolds. Even though it often happens that such theories have a low-energy gauge theory phase, because the gauge coupling in five dimensions is an irrelevant parameter these SCFTs are intrinsically nonlagrangian. In this talk I will show how to extract detailed information about their BPS sector from the geometry of the toric Calabi-Yau, by the introduction of an associated graph, called a quiver. The quiver defines a discrete integrable system, whose solution detemines the string coupling constant corrections to the Seiberg-Witten theory of the low-energy five-dimensional gauge theory: this gives both q-difference equations satisfied by the partition function of the five-dimensional theory compactified on a compact circle with finite radius, and its BPS spectrum.

Eight-dimensional ADHM construction and orbifold DT invariants

We study the moduli space of solutions to the eight-dimensional version of the self-duality equations. We construct a Topological Field Theory describing the dynamics of D(-1)/D7 brane systems on Riemannian manifolds with Spin(7)-holonomy, whose BPS-bound states counting reproduces the Donaldson-Thomas theory on four-folds. An ADHM-like construction provides solutions to SU(4)-invariant first order Yang-Mills equations in eight dimensions which generalise the self-duality equations in four dimensions. The construction can be generalised to orbifolds by the action of a finite subgroup of SU(4), admitting crepant resolutions, whose partition function conjecturally encodes orbifold DT invariants.

ABCDEFG of Gauge and Painlevé

There is a well-known dictionary between N=2 theories and integrable systems. On the other hand, these isospectral systems on the UV curve have a well defined lift to isomonodromic ones, from which in turn the special functions bearing Painlevé's name originate. We show how this dynamical 2d/4d correspondence in a nonconformal limit gives us a very simple way to solve the gauge theory. All we have to do is provide the form of the expansion by fixing the classical action. The rest, everything from the beta function to all-order gravitational corrections of the prepotential on the self-dual graviphoton background, then follows.

Latitude Wilson loop in ABJM theory and dual line operators

I will discuss the dual-line operators associated with a class of BPS Wilson loops in N=4 Chern-Simons matter theories. For ABJM, it is known as latitude and is related to the displacement operator of the 1/2-BPS Wilson loop. I will derive its matrix model from a new localization scheme. I will realize the latitude as a mixed Wilson-vortex loop describing it as a supersymmetric quantum mechanics.

BRST-Lagrangian Double Copy of Yang-Mills Theory

After a review of color-kinematic duality and double copy prescription, we propose an off-shell, Lagrangian perspective on the duality between gauge theories and gravity. We first explain that color–kinematic duality is a condition for the BRST operator and the action of a field theory with cubic interaction terms to double copy to a consistent gauge theory. For Yang-Mills theory, color–kinematic duality is satisfied onshell at tree level. Unphysical gluons and ghosts could potentially lead to violations of color-kinematic duality, but we show that these terms can be absorbed in a sequence of field redefinitions, rendering the double copied action equivalent to N=0 supergravity. In particular, the double copy of gauge theory amplitudes to N=0 supergravity amplitudes extends from tree level to loop level.

Mellin Transform in 1D CFTs: Motivation and Definition

In the context of one-dimensional CFTs, I am going to introduce a simpler representation of correlation functions, namely a new definition of Mellin Transform, describing its essential properties and the interest behind it. Explicit applications and further comments are discussed in Gabriel Bliard’s short talk.

The Holographic Swampland

We investigate whether Swampland constraints on the low-energy dynamics of weakly coupled string vacua in AdS can be related to inconsistencies of their putative holographic duals or, more generally, recast in terms of CFT data. In the first part, we shall illustrate how various swampland consistency constraints are equivalent to a negativity condition on the sign of certain mixed anomalous dimensions. This condition is similar to established CFT positivity bounds arising from causality and unitarity, but not known to hold in general. Our analysis will include LVS, KKLT, perturbative and racetrack stabilisation, and we shall also point out an intriguing connection to the Distance Conjecture. In the second part, we show how a different, recently derived inequality on mixed anomalous dimensions maps to novel constraints on four-derivative interactions on AdS. As an application, we find that the DBI action for multiple scalars is at the boundary of the allowed region.

Thermalization of the Stress Tensor Sector

In d-dimensional CFTs with a large number of degrees of freedom an important set of primary operators is comprised out of the stress tensor and its products, multi stress tensors. We argue that the thermal expectation value of all such operators on the (d-1)-sphere equals their expectation value in a heavy state, therefore, the stress tensor sector satisfies the Eigenstate Thermalization Hypothesis. This is equivalent to the universal leading behavior of the OPE coefficients of multi stress tensors with a pair of identical scalar operators in the limit of large conformal dimensions of the scalars. We verify this in a number of examples which include holographic and free CFTs. We check the thermalization of the stress tensor sector directly by computing thermal expectation values of multi stress tensor operators in a free CFT.

Light-ray operators and gravitational wave detectorsv

We will introduce light-ray operators in a general QFT for massless particles of integer spin, as defined at null infinity. We will derive their algebra- which is in agreement with Cordova and Shao- and we will consider the extension of standard event shapes to the gravitational case, which is of current interest.

Infrared duality in Unoriented Pseudo del Pezzo

We study the orientifold projections of the N = 1 superconformal field theories describing D3-branes probing the Pseudo del Pezzo singularities PdP3b and PdP3c. The PdP3c parent theory admits two inequivalent orientifolds. Exploiting a maximization, we find that one of the two has an a-charge smaller than what one would expect from the orientifold projection, which suggests that the theory flows to the fixed point in the infrared. Surprisingly, the value of a coincides with the charge of the unoriented PdP3b and we interpret this as the sign of an infrared duality.

Dynamical Tadpoles and Weak Gravity Constraints

Non-supersymmetric string models are plagued with tadpoles for dynamical fields, which signal uncanceled forces sourced by the vacuum. We argue that in certain cases, uncanceled dynamical tadpoles can lead to inconsistencies with quantum gravity, via violation of swampland constraints. We describe an explicit realization in a supersymmetric toroidal Z_2xZ_2 orientifold with D7-branes, where the dynamical tadpole generated by displacement of the D7-branes off its minimum leads to violation of the axion Weak Gravity Conjecture. In these examples, cancellation of dynamical tadpoles provides consistency conditions for the configuration, of dynamical nature (as opposed to the topological conditions of topological tadpoles, such as RR tadpole cancellation in compact spaces). We show that this approach provides a re-derivation of the Z-minimization criterion for AdS vacua giving the gravitational dual of a-maximization in 4d N=1 toric quiver SCFTs.

Singular Calabi-Yau threefolds: Springer resolution and quiver gauge theories

Calabi-Yau threefolds with point-like singularities have proven to be a fruitful environment to study the gauge theories of branes sitting on top of the singular points. A particular class of such threefolds can be obtained by appropriately slicing the family of deformations of an ADE singularity, described by its related Dynkin diagram. The Calabi-Yau that arises from the slice carries singularities that correspond at most to the Dynkin diagram. We are interested in finding a systematic way of (partially) resolving these singularities, as well as studying the gauge theories of D5-branes wrapping the resolved cycles by extracting the superpotential of their 4d reduction. Making use of the non-standard method of Springer resolutions we show how to achieve this result in controlled setups, such as the $A_n$ singularities and Reid's pagoda, exhibit a new example of Calabi-Yau threefold with a $D_4$ singularity and finally hint at possible connections of this formalism with T-branes.

Protected Spectrum in $AdS3xS3xT4$

I will discuss my work with Dr. Bogdan Stefanski, Dr. Alessandro Torielli, and Dr. Olof Ohlsson Sax related to computation of the protected spectrum in $AdS3xS3xT4$ and $AdS3xS3xK3$ backgrounds using Algebraic Bethe Ansatz techniques. This includes the analysis of both pure RR and mixed flux backgrounds.

Entanglement and symmetry resolution in two dimensional free quantum field theories

Symmetries are a pillar of modern physics and an evergreen research topic is the characterisation of how the presence of a symmetry influences the properties of a physical system. In particular, I will present an analysis of the entanglement entropies related to different symmetry sectors of free quantum field theories with an internal U(1) symmetry. I will focus on Dirac and complex scalar fields in two spacetime dimensions, both in the massive and massless cases. The main finding is the so-called entanglement equipartition, i.e. at the leading order the entanglement entropy is equally distributed among the different sectors. Thus, the presence of the mass does not spoil this result already found in conformal field theory.

Free-fermion conditions in the context of AdS/CFT

In this talk I will highlight the importance of the free-fermion conditions in the context of AdS/CFT. All holographic integrable models of 8-vertex (or less) type satisfy this condition. By using a diagonalisation procedure on the 6-vertex type model, I will give the explicit expression of the diagonal transfer matrix in manifest free-fermion form for arbitrary number of sites and inhomogeneities. This suggestive result gives the eigenvectors manifestly and can be considered as a powerful alternative to the Algebraic Bethe Ansatz.

$T \bar{T}$-deformation of $q$-Yang-Mills theory

I will present the $T \bar{T}$-perturbed version of $q$-deformed two-dimensional Yang-Mills theory. I will show that the $T \bar{T}$-operator spoils the factorization into chiral/anti-chiral sectors. On the other hand, it preserves a large N third order phase transition, although modifying the phase diagram. Implications for the entanglement entropy at large N will be discussed as well. I will conclude with comments on the potential applications of these results to integrability and to four-dimensional supersymmetric Yang-Mills theory. Based on joint work with Richard J. Szabo and Miguel Tierz [arXiv:2009.00657]

Electromagnetic Quasitopological Gravities

We identify a set of higher-derivative extensions of Einstein-Maxwell theory that allow for spherically symmetric charged solutions characterized by a single metric function. These theories are a non-minimally coupled version of the recently constructed Generalized Quasitopological gravities. We study magnetically-charged black hole solutions in these new theories and we find that for some of them the equations of motion can be fully integrated. In those cases we show that, quite generally, the singularity at the core of the black hole is removed by the higher-derivative corrections, obtaining a globally regular geometry. For all theories, black hole thermodynamics can be studied analytically and we check that the first law holds exactly and that the Euclidean and Noether-charge methods yield the same results. We study extremal black holes and show that they might not exist below a certain mass and that they do not need to represent the minimal mass state for a given charge.

M2- and D3-branes wrapped on a spindle

We consider the Plebanski-Demianski family of solutions of minimal gauged supergravity in d=4, which describes an accelerating, rotating and charged black-hole in AdS4. The 4d metric has conical singularities, but we show that it can uplifted to a completely regular solution of d=11 supergravity. We focus on the supersymmetric and extremal case, where the near-horizon geometry is AdS2x\Sigma, where \Sigma is a spindle, or weighted projective space. We argue that this is dual to a d=1, N=(2,0) SCFT which is the IR limit of a 3d SCFT compactified on a spindle. This, in turn, should be realized holographically by wrapping a stack of M2-branes on a spindle. Such construction displays two interesting features: 1) supersymmetry is realized in a novel way, which is not the topological twist, and 2) the R-symmetry of the d=1 SCFT mixes with the U(1) isometry of the spindle. A similar idea also applies to a class of AdS3x\Sigma solutions of minimal gauged supergravity in five dimensions.

All loop structures in Supergravity Amplitudes on AdS5xS5 from CFT

In this short talk I will discuss some interesting structures appearing in the four-point function of dimension two, protected operators in N=4 SYM, with gauge group SU(N) at infinite ‘t Hooft coupling and in a large N expansion. These structures can be extracted from tree-level CFT data and in a specific limit can be mapped to quantities present in the four-graviton amplitude in flat space type IIB supergravity. In particular, I will show that there exists a one-to-one correspondence between higher logarithmic terms in the CFT correlator and iterated s-channel cuts in the dual amplitude.

Black hole entropy from superconformal indices and a glimpse of black holes in AdS_5 x T^{1,1}

The large N limit of the four-dimensional superconformal index has been computed and successfully compared to the entropy of a class of AdS_5 black holes only in the particular case of *equal* angular momenta. Using the Bethe ansatz formulation of the index, we found a particular universal contribution to the sum over Bethe vacua that correctly leads to the entropy of BPS Kerr–Newman black holes in AdS_5 x S^5 for *arbitrary* values of the conserved charges, thus completing the microscopic derivation of their microstates. We also consider theories dual to AdS_5 x SE_5, where SE_5 is a Sasaki–Einstein manifold. In particular, we explicitly constructed the near-horizon geometry of as yet unkown BPS Kerr–Newman black holes in AdS_5 x T^{1,1}. The entropies of these black holes were computed using the attractor mechanism and we found complete agreement with predictions from the index.

Moduli Stabilisation and the Statistics of SUSY Breaking in the Landscape

In this talk I point out that the inclusion of the Kähler moduli is crucial to understand the distribution of the supersymmetry breaking scale in the landscape since in general one obtains unstable vacua when the F-terms of the dilaton and the complex structure moduli are larger than the F-terms of the Kähler moduli. After taking Kähler moduli stabilisation into account, the distribution of the gravitino mass and the soft terms is found to be power-law in KKLT and perturbatively stabilised vacua which therefore favour high scale supersymmetry. On the other hand, LVS vacua feature a logarithmic distribution of soft terms and thus a preference for lower scales of supersymmetry breaking. Whether the landscape of type IIB flux vacua predicts a logarithmic or power-law distribution of the supersymmetry breaking scale thus depends on the relative preponderance of LVS and KKLT vacua.

On de Sitter string vacua from anti-D3-branes in the Large Volume Scenario

The observation that our universe is in a period of accelerated expansion has led, in the latest years, to many efforts to obtain de Sitter space from String Theory. One of the most studied approaches towards this problem is the KKLT scenario, which relies in the introduction of antibranes in type IIB flux compactifications as a crucial ingredient to stabilise all the moduli in a metastable de Sitter vacuum. The analysis of this kind of models is, in general, quite involved as several non-trivial ingredients of string compactifications need to be considered and tensions arise between the many consistency conditions that must be satisfied. I will illustrate these features in an explicit Calabi Yau orientifold with two Kahler moduli and an anti-D3-brane on top of an O3-plane at the tip of a warped throat of Klebanov-Strassler type, in the Large Volume Scenario. Here, all the moduli can be stabilised with positive vacuum energy, and all the consistency conditions can be fulfilled.

Inception Neural Networks for Complete Intersection Calabi-Yau Manifolds

Recent developments in AI and computer vision led to an improved understanding of deep learning as an efficient method to elaborate, process and learn patterns in data. In this framework a wide class of problems has been tackled using better performing convolutional neural networks. We deal with the prediction of Hodge numbers of Complete Intersection Calabi-Yau 3-folds using such an approach. We introduce a new deep learning architecture inspired by Google's Inception network capable of reaching 97% accuracy for $h^{1,1}$ with only 30% of the data and almost perfect accuracy with 80% of the samples, thus showing the feasibility of deep learning as a predictive method for string theory. We study the improvements introduced by the model and compare its working principles to other state-of-the-art architectures. The model represents a large upgrade on previous attempts and holds potential for different applications to theoretical physics, algebraic topology and geometric deep learning.

Harmonic Hybrid Inflation

I will present a mechanism for realising hybrid inflation using two axion fields with a purely non- perturbatively generated scalar potential. I will show that harmonic hybrid inflation produces observationally viable slow-roll inflation for a wide range of initial conditions. This is possible while accommodating certain Swampland arguments. After discussing briefly some interesting phenomenological features of the model, I will outline several avenues towards realising harmonic hybrid inflation in type IIB string theory.