The Arnold Sommerfeld Center for Theoretical Physics (ASC) in Munich regularly organizes workshops and conferences on special topics in theoretical physics, sometimes in collaboration with other institutes in Munich, like the Max Planck Institute for Physics (MPP). A selection can be found in this channel.
The Arnold Sommerfeld Center for Theoretical Physics (ASC)
Online Workshop on Quantum Gravity, Holography and Quantum Information
Online Workshop on Quantum Gravity, Holography and Quantum Information
The study of quantum effects on black holes including their gravitational backreaction is an important but notoriously hard problem. I will begin by reviewing how the framework of braneworld holography allows to solve it for strongly-coupled quantum conformal fields. Then I will describe a holographic construction of quantum rotating BTZ black holes (quBTZ) using an exact dual four-dimensional bulk solution. Besides yielding the quantum-corrected geometry and the renormalized stress tensor of quBTZ, we use it to show that the quantum black hole entropy, which includes the entanglement of the fields outside the horizon, rather non-trivially satisfies the first law of thermodynamics, while the Bekenstein-Hawking-Wald entropy does not.
We introduce the concept of saturons, systems that saturate a certain bound on entropy, which is imposed by S-matrix and unitarity. Such objects share certain niversal properties (e.g., the area-law of entropy, near-thermal emission, inner entanglement, ...) that goes well beyond gravity. We give an example from QCD. We show that black holes and de Sitter are saturons and this determines their physical properties such as their entanglement curves. Both exhibit anomalous quantum break-time which for de Sitter is deadly. Through this mechanism, the S-matrix formulation of quantum gravity/string theory excludes de Sitter vacua.
I will describe the four-derivative corrections to four-dimensional N=2 minimal gauged supergravity and show that they are controlled by two constants. Interestingly, the solutions of the equations of motion in the two-derivative theory are not modified by the higher-derivative corrections. I will use this to arrive at a general formula for the regularized on-shell action for any asymptotically locally AdS_4 solution of the theory and show how the higher-derivative corrections affect black hole thermodynamic quantities in a universal way. I will employ these results in the context of holography to derive new explicit results for the subleading corrections in the large N expansion of supersymmetric partition functions on various compact manifolds for a large class of three-dimensional SCFTs arising from M2- and M5-branes. I will also briefly discuss possible extensions and generalizations of these results.
Computational complexity is a notion from information theory, initially defined for finite-dimensional systems, measuring the number of gates that have to be applied to a given reference state to reach a target state. Susskind's proposals for defining computational complexity also for characterising quantum properties black holes have triggered significant interest in defining computational complexity also for quantum field theories, i.e. for infinite-dimensional Hilbert spaces. The idea is to establish a precise holographic dictionary for complexity. There are successful proposals for complexity definitions in free quantum field theory. Recently, there have been several proposals also for interacting theories, mostly in the context of conformal field theories, building gate sets from symmetry generators. Questions to be discussed include, in addition to further questions about the talks on the subject presented at the workshop: - What is the status of defining complexity for interacting field theories? - How do different proposals for gate sets, reference states and cost functions compare to each other? - What is the status of establishing a holographic dictionary? - What are promising avenues to be pursued for further progress?
The principle of holography of information states that, in any theory of quantum gravity, a copy of all the information available on a Cauchy slice is also available near the boundary of the slice. This principle can be made precise and proved, under weak assumptions, for theories of gravity in AdS and in flat space and it has interesting implications for black holes. In this talk, we will describe how this principle can be tested within the realm of low-energy effective field theory. We will describe how observers placed in a low-energy state near the boundary of AdS can use a simple physical protocol to completely identify the state of the bulk without directly visiting the bulk. We will also describe low-energy thought experiments that can be used to similarly obtain information about the bulk state from near the boundary of flat space.
In this talk we calculate the entanglement entropy in the presence of a moving mirror in a CFT. We employ the AdS/BCFT construction to describe a gravity dual of moving mirrors. We will show that the time evolution of entanglement entropy for a class of moving mirror, which models an evaporating black hole, follows an ideal page curve. In this gravity dual of this model and also in earlier works on holographic page curves, the end of the world-brane in AdS plays a crucial role. I will also present our recent result on their chaotic spectrum in holographic CFTs.
In this talk I will discuss circuit complexity in the setting of higher dimensional conformal field theories. I will consider unitary gates built from a representation of the conformal group, two different circuit cost functions defined using either the Fubini-Study metric or the one-norm, and paths that start from an initial spinless primary state. We will see that the resulting Fubini-Study metric is the metric on a particular coadjoint orbit of the conformal group, while the one-norm computes the geometric action associated to this orbit. This generalizes recent results in 2d connecting the one-norm to a Virasoro geometric action, and also shows that coadjoint orbits provide a unified geometric framework that applies to different choices of cost functions. I will end with some comments about symmetry groups other than the conformal group, using group theoretic generalizations of coherent states. This is based on a work with Nicolas Chagnet, Jan de Boer and Claire Zukowski.
Computational complexity is a quantum information concept that recently has found applications in holography. I will consider quantum computational complexity for n qubits using Nielsen's geometrical approach. In the definition of complexity there is a big amount of arbitrariness due to the choice of the penalty factors, which parameterize the cost of the elementary computational gates. In order to reproduce desired features in holography, negative sectional curvatures are required. With the simplest choice of penalties, this is achieved at the price of singular curvatures in the large n limit. I will consider a choice of penalties in which negative curvatures can be obtained in a smooth way. I will also talk about the relation between operator and state complexities, framing the discussion in the language of Riemannian submersions. Finally, I'll discuss conjugate points for a large number of qubits in the unitary space and I'll provide a strong indication that maximal complexity scales exponentially with the number of qubits in a certain regime of the penalties space.
I will present the connection between the Wheeler-DeWitt approach for two-dimensional quantum gravity and holography, focusing in the case of Liouville theory coupled to c = 1 matter. The analysis is in a spirit similar to the recent studies of Jackiw-Teitelboim gravity. Matrix quantum mechanics and the associated double scaled fermionic field theory, are providing the complete dynamics of such two-dimensional universes with c=1 matter, including the effects of topology change.
The pole skipping phenomenon is a subtle effect in the thermal energy density retarded two point function at a special point in the complex frequency and momentum planes. For maximally chaotic theories, this special point is related to data characterising the butterfly effect, and is explained by a common dynamical origin of energy transport and scrambling. I will argue that pole skipping also happens in non-maximally chaotic theories and its location corresponds to the stress tensor contribution to many body chaos. I will test this proposal in the large q limit of an SYK chain, where I determine both the Lyapunov growth of the OTO correlator and the energy density two point function exactly as a function of the coupling, interpolating between weekly coupled and maximally chaotic behaviour.
A salient feature of black holes near extremality is the appearance of an AdS2 throat in their near-horizon geometry. Depending on the underlying theory, these AdS2 throats may be unstable to fragmentation, wherein a single throat is instead replaced by a tree-like structure of branched AdS2 throats. For Einstein-Maxwell theory, the underlying reason behind this instability is the existence of multi-centered configuration in the moduli space of black hole solutions at fixed total charge. Given the success of the Schwarzian/SYK paradigm for understanding a single AdS2 it is time to revisit the fragmentation story. To build up intuition, I will present a model, studied in the statistical mechanics literature, that shares many features with SYK, including exact solvability at large-N and an emergent conformal symmetry that gets weakly broken in the UV. The novel feature of this model is the appearance of a spin glass phase at O(1) temperatures, which I will try to relate to the fragmentation story.
Domain walls between Anti-de Sitter vacua are important for the study of the string-theory landscape, and enter in recent toy models of black hole evaporation. In this talk I will describe the phase diagram of a simple 2+1 dimensional model of thin domain walls anchored at the AdS boundary, and I will comment on its dual holographic interpretation.
Euclidean wormholes comprise exotic types of gravitational solutions, that still challenge our physical intuition and understanding. In the first part of the talk, I will analyse asymptotically AdS wormhole solutions in the context of holography. From a bottom up perspective a study of correlation functions of local and non-local operators indicates the universal properties that any putative holographic dual should exhibit. The system is very weakly cross-coupled in the UV, and becomes strongly cross-coupled in the IR. In the second part, I will describe some concrete field theoretic setups which exhibit such a behaviour and comment on various issues arising in the alpha-parameter interpretation of the wormhole gas.
We consider the effect of shockwaves on the entanglement structure of black holes. We examine the correlations in generic subsets of the Hawking radiation emitted by evaporating black holes following the shockwave insertion and find a zoo of competing island saddle points for the associated entanglement entropies. By computing the mutual information between early and late modes we establish long range correlations in the Hawking radiation.
Quantum Complexity, Integrability, and Chaos The states of quantum systems grow in complexity over time as entanglement spreads between degrees of freedom. Following ideas in computer science, we formulate the complexity of evolution as the length of the shortest geodesic on the unitary group manifold between the identity and the time evolution operator, and use the SYK family of models with N fermions to study this quantity in free, integrable, and chaotic systems. In all cases, the complexity initially grows linearly in time, and the shortest path lies along the physical time evolution. This linear growth is eventually truncated by "shortcuts" on the unitary manifold that are shorter than the physical time evolution. We explicitly locate such shortcuts and hence show that in the free theory, shortcuts occur at a time of O(N^1/2), truncating complexity growth at this scale. We also find an explicit operator which "fast-forwards" time evolution with this complexity. In a class of integrable theories, we show that shortcuts appear in a time upper bounded by O(poly(N)), again truncating complexity growth. Finally, in chaotic theories we argue that shortcuts do not occur until exponential times, after which it becomes possible to find infinitesimally nearby fixed-complexity approximations to the time evolution operator. We relate these results to the Eigenstate Complexity Hypothesis, a new criterion on the spectrum of energy eigenstates that guarantees an exponential increase of complexity over time that is consistent with maximal chaos.
Recent developments in holography indicate that the semi-classical Euclidean path-integral of Einstein gravity is much more powerful than previously anticipated. It is capable of reproducing a unitary Page curve for black hole evaporation, and can even capture some features of the discrete nature of black hole microstates. Wormhole geometries play a key role in this context. I will propose a mechanism to explain this in the CFT: the OPE Randomness Hypothesis. This ansatz is a generalization of the Eigenstate Thermalization Hypothesis which applies to chaotic CFTs, and treats OPE coefficients of heavy operators as random variables with a given probability distribution. I will present two applications of this framework: First, it resolves a factorization puzzle in AdS_3/CFT_2 due to the genus-2 wormhole, as raised by Maoz and Maldacena. Second, it provides an argument against global symmetries in quantum gravity.
I present evidence, both from a GR and a holographic viewpoint, that Coleman's Euclidean axion wormholes do not contribute to the path integral.
Given that exact global symmetries are forbidden by quantum gravity, it is natural to expect that bounds on the quality of approximate global symmetries exist. So far, holographic arguments have only been provided for the former claim. I will discuss a classification of approximate global symmetries and describe a simple argument, based the Weak Gravity Conjecture, for a quantitative bound on the sub-class of "gauge-derived" global symmetries. This has intriguing relations to wormhole-based arguments, which I will also present. I will end with a brief discussion of the fundamental problems associated with euclidean wormholes and of some recent developments in this context.
I will review some recent progress on six-dimensional conformal field theories, highlighting applications to the dynamics of M5-branes. On an orbifold singularity, M5s can fractionate, and they can recombine by sometimes leaving behind a 'frozen' version of the singularity. The CFTs describing these processes also happen to be ubiquitous building blocks for more complicated ones. There is also evidence for other processes where branes recombine in patterns associated to nilpotent orbits of Lie groups, with precise checks obtained by anomalies and moduli space dimensions.
ASC Workshop: Fields and Duality 2017
The talks will focus on half-BPS boundary conditions for 3d N=2 gauge theories that preserve 2d N=(0,2) supersymmetry. I will review (and extend) the classification of such boundary conditions and the BPS local operators living on them, which form chiral algebras. I define a half-index that counts boundary local operators, or equivalently computes a character of the boundary chiral algebra. With the help of the half-index and some physical intuition, I will identify the action on boundary conditions of some basic dualities, including ``mirror symmetries'' and level-rank dualities. This in turn leads to a definition of duality interfaces. (Work in progress with D. Gaiotto and N. Paquette.)
As a consequence of electric-magnetic duality, partition functions of four-dimensional gauge theories can be expressed in terms of modular forms in many cases. I will discuss new results for the modularity of topologically twisted partition functions of N=2 and N=4 supersymmetric theories, and in particular how these partititon functions may involve (iterated) integrals of modular forms.
ASC Workshop: Fields and Duality 2017
The gauge origami are the statistical mechanical models which arise from supersymmetric localisation of gauge theory path integrals. I will describe the gauge theory problems which lead to these models, and time permitting will explain the connection to quantum algebras and integrable systems.
After recalling how some 4d N=2 gauge theories arise from reductions of 6d N=(2,0) superconformal theories on a Riemann surface, I will discuss two discrete quotients with codimension 2 orbifold singularities. In the first case the orbifold acts by rotations around one plane of the 4d N=2 theory; this is related to a Gukov-Witten surface operator that imposes a monodromy around that plane. We deduce instanton partition functions in the presence of surface operators; interestingly, instantons can fractionalize. In the second case the orbifold acts by reflection on the 4d theory and the Riemann surface. We learn how boundaries are encoded in the AGT correspondence. We are led to consider 4d N=2 quiver theories where some vector multiplets live on a hemisphere and others on a projective space.
We explore 1d vortex dynamics of 3d supersymmetric Yang-Mills theories, as inferred from factorization of exact partition functions. Under Seiberg-like dualities, the 3d partition function must remain invariant, yet it is not a priori clear what should happen to the vortex dynamics. We observe that the 1d quivers for the vortices remain the same, and the net effect of the 3d duality map manifests as 1d Wall-Crossing phenomenon; Although the vortex number can shift along such duality maps, the ranks of the 1d quiver theory are unaffected, leading to a notion of fundamental vortices as basic building blocks for topological sectors. For Aharony-type duality, in particular, where one must supply extra chiral fields to couple with monopole operators on the dual side, 1d wall-crossings of an infinite number of vortex quiver theories are neatly and collectively encoded by 3d determinant of such extra chiral fields.
The talks will focus on half-BPS boundary conditions for 3d N=2 gauge theories that preserve 2d N=(0,2) supersymmetry. I will review (and extend) the classification of such boundary conditions and the BPS local operators living on them, which form chiral algebras. I define a half-index that counts boundary local operators, or equivalently computes a character of the boundary chiral algebra. With the help of the half-index and some physical intuition, I will identify the action on boundary conditions of some basic dualities, including ``mirror symmetries'' and level-rank dualities. This in turn leads to a definition of duality interfaces. (Work in progress with D. Gaiotto and N. Paquette.)
I will present recent results about supersymmetric partition functions of 3d N=2 and 4d N=1 supersymmetric gauge theories with an R-symmetry. Many partition function functions on half-BPS geometric backgrounds can be viewed as expectation values of codimension-2 half-BPS defect operators on C*S^1 (in 3d) or C*T^2 (in 4d), with C a Riemann surface. This approach greatly simplifies previous computations, and leads to new results.
We study compactifications of the 6d E-string theory, the theory of a small E_8 instanton, to four dimensions. In particular we identify N=1 field theories in four dimensions corresponding to compactifications on arbitrary Riemann surfaces with punctures and with arbitrary non-abelian flat connections as well as fluxes for the abelian sub-groups of the E_8 flavor symmetry. This sheds light on emergent symmetries in a number of 4d N=1 SCFTs (including the `E7 surprise' theory) as well as leads to new predictions for a large number of 4-dimensional exceptional dualities and symmetries.
I discuss how localization techniques for three and four-dimensional supersymmetric gauge theories can lead to a microscopic entropy counting for AdS black holes.
Every N=2 SCFT in four dimensions comes equipped with a vertex operator algebrathat encodes the spectrum and OPE coefficients of an infinite class of 1/4 BPS operators knownas Schur operators. I will discuss a number of results as well as open questions regarding thestructural properties of the VOAs that appear in this correspondence and their relationship to four-dimensional physics. I will discuss a proposal for how to recover of the Higgs branch ofvacua from the VOA and the consequences of this proposal for the behaviour of Schur superconformal indices under modular transformations. This leads to a surprising relationship between the a-type Weyl anomaly coefficient and the spectrum of surface operators in an N=2 SCFT.
I will present a new approach to study the RG flow in 3d N=4 gauge theories, based on an analysis of the Coulomb branch of vacua, focusing on U(N) SQCD theories with fundamental matter. The Coulomb branch is described as a complex algebraic variety and important informations about the strongly coupled fixed points of the theory can be extracted from the study of its singularities. I will use this framework to revisit and clarify the classification of infrared fixed points in U(N) SQCD with different amounts of matter hypermultiplets, in particular for the so called ``bad" theories.
Gauge/Gravity Duality 2013
Gauge/Gravity Duality 2013
Gauge/Gravity Duality 2013
Gauge/Gravity Duality 2013
Gauge/Gravity Duality 2013
Gauge/Gravity Duality 2013
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