Past String Theory Seminar

In this talk I will discuss a novel mechanism  that couples matter fields to three-dimensional de Sitter quantum gravity. This construction is based on the Chern-Simons formulation of three-dimensional Euclidean gravity, and it centers on a collection of Wilson loops winding around Euclidean de Sitter space. We coin this object a Wilson spool.  To construct the spool, we build novel representations of su(2). To evaluate the spool, we adapt and exploit several known exact results in Chern-Simons theory. Our proposal correctly reproduces the one-loop determinant of a free massive scalar field on S^3 as G_N->0. Moreover, allowing for quantum metric fluctuations, it can be systematically evaluated to any order in perturbation theory.   

We propose new G2-holonomy manifolds, which geometrize the Gaiotto-Kim 4d N = 1 duality
domain walls of 5d N = 1 theories. These domain walls interpolate between different extended
Coulomb branch phases of a given 5d superconformal field theory. Our starting point is the
geometric realization of such a 5d superconformal field theory and its extended Coulomb
branch in terms of M-theory on a non-compact singular Calabi-Yau three-fold and its Kahler
cone. We construct the 7-manifold that realizes the domain wall in M-theory by fibering the
Calabi-Yau three-fold over a real line, whilst varying its Kahler parameters as prescribed by
the domain wall construction. In particular this requires the Calabi-Yau fiber to pass through
a canonical singularity at the locus of the domain wall. Due to the 4d N = 1 supersymmetry
that is preserved on the domain wall, we expect the resulting 7-manifold to have holonomy G2.
Indeed, for simple domain wall theories, this construction results in 7-manifolds, which are
known to admit torsion-free G2-holonomy metrics. We develop several generalizations to new
7-manifolds, which realize domain walls in 5d SQCD theories.

I will present results from arXiv:2202.13924, where we studied the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. The notion of complexity of interest to us will be Nielsen’s complexity applied to the time-dependent evolution operator of the quantum systems. I will review Nielsen’s complexity, discuss the difficulties associated with this definition and introduce a simplified approach which appears to retain non-trivial information about the integrable properties of the dynamical systems.

A 2d SCFT given as a non-linear sigma model of a Ricci-flat Kahler target 

space is not a rational CFT in general; only special points in the moduli 

space of the target-space metric, the 2d SCFTs are rational. 

Gukov-Vafa's paper in 2002 hinted at a possibility that such special points 

may be characterized by the property "complex multiplication" of the target space, 

which has its origin in number theory. We revisit the idea, refine the Conjecture, 

and prove it in the case the target space is T^4. 
 

This presentation is based on arXiv:2205.10299 and 2212.13028 .

5d Superconformal Field Theories (SCFTs) are intrinsically strongly-coupled UV fixed points, whose realization hinges on string theoretic methods: they can be constructed by compactifying M-theory on local Calabi-Yau threefold singularities or alternatively from the world-volume of 5-brane-webs in type IIB string theory. There is a correspondence between 5-brane-webs and toric Calabi-Yau threefolds, however this breaks down when multiple 5-branes are allowed to end on a single 7-brane. In this talk, we extend this connection and provide a geometric realization of brane configurations including 7-branes. Along the way, we also review techniques developed in the past few years to describe the Higgs branch of these 5d SCFTs, including magnetic quivers and Hasse diagram for symplectic singularities. 

In her recent work, Mina Aganagic proposed novel perspectives on computing knot homologies associated with any simple Lie algebra. One of her proposals relies on counting intersection points between Lagrangians in Landau-Ginsburg models on symmetric powers of Riemann surfaces. In my talk, I am going to present a concrete algebraic algorithm for finding such intersection points, turning the proposal into an actual calculational tool. I am going to illustrate the construction on the example of the sl_2 invariant for the Hopf link. I am also going to comment on the extension of the story to homological invariants associated to gl(m|n) super Lie algebras, solving this long-standing problem. The talk is based on our work in progress with Mina Aganagic and Elise LePage.

When do two quantum field theories describe the same physics? I will discuss some approaches to this question in the context of superconformal field theories in four and six dimensions. First, I will discuss the construction of 6d (1,0) SCFTs from the perspective of the "atomic classification", focussing on an oft-overlooked subtlety whereby distinct SCFTs in fact share an effective description on the generic point of the tensor branch. We will see how to determine the difference in the Higgs branch operator spectrum from the atomic perspective, and how that agrees with a dual class S perspective. I will explain how other 4d N=2 SCFTs, which a priori look like distinct theories, can be shown to describe the same physics, as they arise as torus-compactifications of identical 6d theories.

In recent progress on the black hole information paradox, Page curves consistent with unitarity have been obtained in 2d models and in bottom-up braneworld models using the notion of double holography. In this talk we discuss top-down models realizing 4d black holes coupled to a bath in Type IIB string theory and obtain Page curves. We make the ideas behind double holography precise in these models and address causality puzzles which have arisen in the bottom-up models, leading to a refinement of their interpretation.
 

We study supersymmetric gauge theories with 8 supercharges in d=3,4,5,6. For these theories, one can perform Higgsings by turning on VEVs of scalar fields. However, this process can often be difficult when dealing with superconformal field theories (SCFTs) where the Lagrangian is often not known. Using techniques of magnetic quivers and a new algorithm we call "Inverted Quiver Subtraction", we show how one can easily obtain the SCFT(s) after Higgsing. This technique can be equally well applied to SCFTs in d=3,4,5,6. 

Conformal Field Theories (CFT) are believed to be exactly solvable once their primary scaling fields and their 3-point functions are known. This input is called the spectrum and structure constants of the CFT respectively. I will review recent work where this conformal bootstrap program can be rigorously carried out for the case of Liouville CFT, a theory that plays a fundamental role in 2d random surface theory and many other fields in physics and mathematics. Liouville CFT has a probabilistic formulation on an arbitrary Riemann surface and the bootstrap formula can be seen as a "quantization" of the plumbing construction of surfaces with marked points axiomatically discussed earlier by Graeme Segal. Joint work with Colin Guillarmou, Remi Rhodes and Vincent Vargas.

After reviewing different aspects of thermalization and chaos in holographic quantum systems, I will argue that universal aspects can be captured using an effective field theory framework that shares similarities with hydrodynamics. Focusing on the quantum butterfly effect, I will explain how to develop a simple effective theory of the 'scramblon' from path integral considerations. I will also discuss applications of this formalism to shockwave scattering in black hole backgrounds in AdS/CFT.

Only a decade ago the detection of gravitational waves seemed like a fantasy to most, and merely a handful of 
people in the world believed in the validity and even great potential of using the powerful framework of EFT, and 
more generally -- advances in QFT to study gravity theory for real-world gravitational waves. I will present the 
significant advancement accomplished uniquely via the tower of EFTs with the EFT of spinning gravitating objects, 
and the incorporation of QFT advances, which my work has pioneered since those days. Today, only 6 years after 
the official birth of precision gravity with a rapidly growing influx of gravitational-wave data, and a decade of great 
theoretical progress, the power and insight of using modern QFT for real-world gravity have become incontestable.

Argyres—Douglas (AD) theories are 4d N=2 SCFTs which have some unusual features, and until recently, explicit holographic duals of these theories were unknown. We will consider a concrete class of these theories obtained by wrapping the 6d N=(2,0) ADE theories on a (twice) punctured sphere: one irregular and one regular puncture, and construct their holographic duals. The novel aspects of these solutions require a relaxation of the regularity conditions of the usual Gaiotto—Maldacena framework and to allow for brane singularities. We show how to construct the dictionary between the AdS(5) solutions and the field theory and match observables between the two. If time allows, I will comment on some on-going work about further compactifying the AD theories on spindles, or the 6d theories on four-dimensional orbifolds. 

I will describe a procedure, known as holomorphic twist, to isolate protected quantities in supersymmetric quantum field theories. The resulting theories are holomorphic, interacting and have infinite dimensional symmetries, analogous to the holomorphic half of a 2D CFT. I will explain how to study quantum corrections to these symmetries and other  higher operations.
As a surprise, we find a novel UV manifestation of
confinement, dubbed "holomorphic confinement," in the example of pure
SU(N) super Yang-Mills.

Quantum field theories (QFTs) in d dimensions that posses a (d-1)-form symmetry are conjectured to decompose into disjoint “universes”, each of which is itself a (local and unitary) QFT. I will give an overview of our current understanding of decomposition, and then discuss how this phenomenon occurs in the fusion of condensation defects of certain 3d QFTs. This gives a “microscopic” explanation of why in these instances, the fusion coefficient can be taken as an integer rather than a general TQFT.

According to the correspondence principle, classical physics emerges in the limit of large quantum numbers. We examine three examples of the semiclassical description of conformal field theory data: large charge boundary operators in the O(2) model, large spin impurities in the free triplet scalar field theory and large charge Wilson lines in QED. By simultaneously taking the coupling to zero and quantum numbers to infinity, we can connect the microscopic to the emergent classical description smoothly.

Liouville conformal field theory models two-dimensional gravity with a cosmological constant and conformal matter. In its timelike regime, it reproduces the characteristic negative kinetic term of the conformal factor of the metric in the Einstein-Hilbert action, the sign which infamously makes the gravity path integral ill-defined. In this talk, I will first discuss the perturbative computation of the timelike Liouville partition function around the sphere saddle and propose an all-orders result. I will then turn to the disk and present the bulk 1-point functions of this CFT, and discuss possible interpretations in terms of boundary conditions.

I will discuss the free compact boson CFT thrown out of equilibrium by marginal deformations, modeled by quenching or periodically driving the compactification radius of the free boson between two different values. All the dynamics will be shown to be crucially dependent on the ratio of the compactification radii via the Zamolodchikov distance in the space of marginal deformations. I will present various exact analytic results for the Loschmidt echo and the time evolution of energy density for both the quench and the periodic drive. Finally, I will present a non-perturbative computation of the  Rényi divergence, an information-theoretic distance measure, between two marginally deformed thermal density matrices.

The talk will be based on the recent preprint: arXiv:2206.11287

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 order 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.

The line operators in a 2+1D TQFT form an algebraic structure called a modular tensor category (MTC). There is a natural action of a Galois group on MTCs which maps a given TQFT to other 'Galois conjugate' TQFTs. I will describe this Galois action and give several examples of Galois conjugate TQFTs. Galois action on a unitary TQFT can result in a non-unitary TQFT. I will derive a sufficient condition under which unitarity is preserved. Finally, I will describe the invariance of 0-form and 1-form symmetries of TQFTs under Galois action.    

Topological defects in quantum field theory can be understood as a generalised notion of symmetry, where the operation is not required to be invertible. Duality transformations are an important example of this. By considering defects of various dimensions, one is naturally led to more complicated algebraic structures than just groups. So-called 2-groups are a first instance, which arise from invertible defects of codimension 1 and 2. Without invertibility one arrives at so-called "fusion categories”. I would like to explain how one can "gauge" such non-invertible symmetries in the case of topological field theories, and I will focus on results in two and three dimensions. This talk is based on joint work with Nils Carqueville, Vincentas Mulevicius, Gregor Schaumann, and Daniel Scherl.