scholarly journals Boundary conditions in topological AdS4/CFT3

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Pietro Benetti Genolini ◽  
Matan Grinberg ◽  
Paul Richmond
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Boundary Conditions ◽  
Smooth Solution ◽  
Three Dimensional ◽  
Field Theories ◽  
Legendre Transformation ◽  
Generating Functional ◽  
Holographic Duals

Abstract We revisit the construction in four-dimensional gauged Spin(4) supergravity of the holographic duals to topologically twisted three-dimensional $$ \mathcal{N} $$ N = 4 field theories. Our focus in this paper is to highlight some subtleties related to preserving supersymmetry in AdS/CFT, namely the inclusion of finite counterterms and the necessity of a Legendre transformation to find the dual to the field theory generating functional. Studying the geometry of these supergravity solutions, we conclude that the gravitational free energy is indeed independent from the metric of the boundary, and it vanishes for any smooth solution.

scholarly journals Thermodynamic limit for a system with dipole-dipole interactions

1975 ◽  
Vol 19 (1) ◽  
pp. 116-128 ◽  
Author(s):  
E. R. Smith ◽  
J. W. Perram
Keyword(s):  
Free Energy ◽  
Variational Principle ◽  
Boundary Conditions ◽  
Thermodynamic Limit ◽  
Periodic Boundary ◽  
Three Dimensional ◽  
Periodic Boundary Conditions ◽  
Free Energies ◽  
Dipole Interactions ◽  
Simple Boundary

AbstractIt is shown that for the three dimensional Ising model with dipole-dipole interactions, the thermodynamic limit of the free energy with simple boundary conditions is not the same as the thermodynamic limit of the free energy with periodic boundary conditions. A variational principle is developed to connect the two free energies.

scholarly journals Conformal Boundary Conditions and Three-Dimensional Topological Field Theory

2000 ◽  
Vol 84 (8) ◽  
pp. 1659-1662 ◽  
Author(s):  
Giovanni Felder ◽  
Jürg Fröhlich ◽  
Jürgen Fuchs ◽  
Christoph Schweigert
Keyword(s):  
Field Theory ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Topological Field Theory ◽  
Conformal Boundary ◽  
Topological Field

scholarly journals On dualizability of braided tensor categories

2021 ◽  
Vol 157 (3) ◽  
pp. 435-483
Author(s):  
Adrien Brochier ◽  
David Jordan ◽  
Noah Snyder
Keyword(s):  
Field Theory ◽  
Quantum Group ◽  
Topological Field Theories ◽  
Characteristic Zero ◽  
Three Dimensional ◽  
Field Theories ◽  
Topological Field Theory ◽  
Tensor Categories ◽  
Fusion Categories ◽  
Topological Field

We study the question of dualizability in higher Morita categories of locally presentable tensor categories and braided tensor categories. Our main results are that the 3-category of rigid tensor categories with enough compact projectives is 2-dualizable, that the 4-category of rigid braided tensor categories with enough compact projectives is 3-dualizable, and that (in characteristic zero) the 4-category of braided multi-fusion categories is 4-dualizable. Via the cobordism hypothesis, this produces respectively two-, three- and four-dimensional framed local topological field theories. In particular, we produce a framed three-dimensional local topological field theory attached to the category of representations of a quantum group at any value of $q$ .

scholarly journals Super-Chern-Simons spectra from exceptional field theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Oscar Varela
Keyword(s):  
Field Theory ◽  
Mass Matrix ◽  
Three Dimensional ◽  
Field Theories ◽  
Specific Class ◽  
Chern Simons ◽  
Kaluza Klein

Abstract Exceptional Field Theory has been recently shown to be very powerful to compute Kaluza-Klein spectra. Using these techniques, the mass matrix of Kaluza-Klein vector perturbations about a specific class of AdS4 solutions of D = 11 and massive type IIA supergravity is determined. These results are then employed to characterise the complete supersymmetric spectrum about some notable $$ \mathcal{N} $$ N = 2 and $$ \mathcal{N} $$ N = 3 AdS4 solutions in this class, which are dual to specific three-dimensional superconformal Chern-Simons field theories.

scholarly journals Non-Supersymmetric CS-Matter Theories with Known AdS Duals

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Davide Forcella ◽  
Alberto Zaffaroni
Keyword(s):  
Field Theory ◽  
Three Dimensional ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Natural Field ◽  
Conformal Field ◽  
Stable Field ◽  
Supergravity Solution

We consider three-dimensional conformal field theories living on a stack ofNanti-M2 branes at the tip of eight-dimensional supersymmetric cones. The corresponding supergravity solution is obtained by changing sign to the four-form in the Freund-Rubin solution representing M2 branes (“skew-whiffing” transformation) and it is known to be stable. The existence of these non-supersymmetric, stable field theories, at least in the largeNlimit, is a peculiarity of theAdS4/CFT3correspondence with respect to the usualAdS5/CFT4, and it is worthwhile to study it. We analyze in detail the KK spectrum of the skew-whiffed solution associated withS7/ℤkand we speculate on the natural field content for a candidate non-supersymmetric dual field theory.

scholarly journals Near horizon dynamics of three dimensional black holes

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Daniel Grumiller ◽  
Wout Merbis
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Einstein Gravity ◽  
Hamiltonian Reduction ◽  
Total Derivative ◽  
Zero Modes ◽  
Derivative Term ◽  
Total Derivative Term

We perform the Hamiltonian reduction of three dimensional Einstein gravity with negative cosmological constant under constraints imposed by near horizon boundary conditions. The theory reduces to a Floreanini–Jackiw type scalar field theory on the horizon, where the scalar zero modes capture the global black hole charges. The near horizon Hamiltonian is a total derivative term, which explains the softness of all oscillator modes of the scalar field. We find also a (Korteweg–de Vries) hierarchy of modified boundary conditions that we use to lift the degeneracy of the soft hair excitations on the horizon.

scholarly journals Modular Hamiltonians in flat holography and (W)AdS/WCFT

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Luis Apolo ◽  
Hongliang Jiang ◽  
Wei Song ◽  
Yuan Zhong
Keyword(s):  
Quantum Gravity ◽  
Entanglement Entropy ◽  
Three Dimensional ◽  
Neumann Boundary ◽  
Field Theories ◽  
Covariant Formulation ◽  
Boundary Field ◽  
Conformal Field ◽  
Holographic Duals ◽  
Holographic Description

Abstract We study several aspects of holographic entanglement in two models known as flat3/BMSFT and (W)AdS3/WCFT. These are two examples of holography beyond AdS/CFT where the boundary field theories are not Lorentz invariant but still feature an infinite set of local symmetries. In the first example, BMS-invariant field theories (BMSFTs) are conjectured to provide a holographic description of quantum gravity in asymptotically flat three-dimensional spacetimes; while in the second example, warped conformal field theories (WCFTs) are proposed to describe quantum gravity in warped AdS3 or AdS3 backgrounds with Dirichlet-Neumann boundary conditions. In particular, we derive the modular Hamiltonian for single intervals in both BMSFTs and WCFTs and find the holographic duals in the bulk using the covariant formulation of gravitational charges. We also extend the first law of entanglement entropy to these models of non-AdS holography and discuss the bound on “modular chaos” introduced recently in the context of the AdS/CFT correspondence.

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