scholarly journals Holographic path-integral optimization

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Jan Boruch ◽  
Pawel Caputa ◽  
Dongsheng Ge ◽  
Tadashi Takayanagi
Keyword(s):  
Excited States ◽  
Path Integral ◽  
Optimization Procedure ◽  
Wave Functions ◽  
Conformal Field Theories ◽  
De Sitter ◽  
Conformal Field ◽  
Holographic Description ◽  
Integral Complexity ◽  
Shed Light

Abstract In this work we elaborate on holographic description of the path-integral optimization in conformal field theories (CFT) using Hartle-Hawking wave functions in Anti-de Sitter spacetimes. We argue that the maximization of the Hartle-Hawking wave function is equivalent to the path-integral optimization procedure in CFT. In particular, we show that metrics that maximize gravity wave functions computed in particular holographic geometries, precisely match those derived in the path-integral optimization procedure for their dual CFT states. The present work is a detailed version of [1] and contains many new results such as analysis of excited states in various dimensions including JT gravity, and a new way of estimating holographic path-integral complexity from Hartle-Hawking wave functions. Finally, we generalize the analysis to Lorentzian Anti-de Sitter and de Sitter geometries and use it to shed light on path-integral optimization in Lorentzian CFTs.

A topological criterion for group decompositions

1988 ◽  
Vol 103 (2) ◽  
pp. 285-298 ◽  
Author(s):  
J. Hebda ◽  
P. Moylan
Keyword(s):  
Asymptotic Properties ◽  
Cartesian Product ◽  
Conformal Field Theories ◽  
De Sitter ◽  
Group Representations ◽  
Conformal Field ◽  
Connected Subgroup ◽  
Closed Connected Subgroup ◽  
Necessary And Sufficient

AbstractGiven a connected Lie group G and a closed connected subgroup H of G we prove a necessary and sufficient condition that G decomposes into the Cartesian product of H with G/H is that a similar decomposition holds for the maximal compact subgroups of G and H. Our criterion is applied to the three series of groups for which G/H is SO0(p, q)/SO0(p, q − 1), SU(q + 1, q + 1)/S[U(q + 1, q) × U(1)], and SU(q + 1, q + 1)/SL(n, ℂ) ⋊ H(n) (p, q ≥ 1), and we list the values of p and q for which G ≅ H × G/H in each of the three cases. We describe certain decompositions for some of the groups. We show the usefulness of our criterion in obtaining characterization of the space of differentiable vectors for a unitary induced group representation, and, finally, we show by example of SU(2, 2), how the asymptotic properties of certain function spaces for induced group representations are readily obtained using our results. Our results should be of interest to those working in de Sitter and conformal field theories.

scholarly journals Holographic BCFTs and communicating black holes

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Hao Geng ◽  
Severin Lüst ◽  
Rashmish K. Mishra ◽  
David Wakeham
Keyword(s):  
Field Theory ◽  
Black Holes ◽  
Central Charge ◽  
Entanglement Entropy ◽  
Three Dimensional ◽  
Conformal Field Theories ◽  
De Sitter ◽  
Conformal Field ◽  
Theory Calculation ◽  
Scaling Dimension

Abstract We study the AdS/BCFT duality between two-dimensional conformal field theories with two boundaries and three-dimensional anti-de Sitter space with two Karch-Randall branes. We compute the entanglement entropy of a bipartition of the BCFT, on both the gravity side and the field theory side. At finite temperature this entanglement entropy characterizes the communication between two braneworld black holes, coupled to each other through a common bath. We find a Page curve consistent with unitarity. The gravitational result, computed using double-holographically realized quantum extremal surfaces, matches the conformal field theory calculation.At zero temperature, we obtain an interesting extension of the AdS3/BCFT2 correspondence. For a central charge c, we find a gap $$ \left(\frac{c}{16},\frac{c}{12}\right) $$ c 16 c 12 in the spectrum of the scaling dimension ∆bcc of the boundary condition changing operator (which interpolates mismatched boundary conditions on the two boundaries of the BCFT). Depending on the value of ∆bcc, the gravitational dual is either a defect global AdS3 geometry or a single sided black hole, and in both cases there are two Karch-Randall branes.

scholarly journals Symmetry-resolved entanglement for excited states and two entangling intervals in AdS3/CFT2

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Konstantin Weisenberger ◽  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Excited States ◽  
Vertex Operator Algebra ◽  
Central Charge ◽  
Entanglement Entropy ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Chern Simons ◽  
Twist Fields

Abstract We test the proposal of [1] for the holographic computation of the charged moments and the resulting symmetry-resolved entanglement entropy in different excited states, as well as for two entangling intervals. Our holographic computations are performed in U(1) Chern-Simons-Einstein-Hilbert gravity, and are confirmed by independent results in a conformal field theory at large central charge. In particular, we consider two classes of excited states, corresponding to charged and uncharged conical defects in AdS3. In the conformal field theory, these states are generated by the insertion of charged and uncharged heavy operators. We employ the monodromy method to calculate the ensuing four-point function between the heavy operators and the twist fields. For the two-interval case, we derive our results on the AdS and the conformal field theory side, respectively, from the generating function method of [1], as well as the vertex operator algebra. In all cases considered, we find equipartition of entanglement between the different charge sectors. We also clarify an aspect of conformal field theories with a large central charge and $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry used in our calculations, namely the factorization of the Hilbert space into a gravitational Virasoro sector with large central charge, and a $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody sector.

scholarly journals Conformal field theories in anti-de Sitter space

2011 ◽  
Vol 2011 (2) ◽  
Author(s):  
Ofer Aharony ◽  
Donald Marolf ◽  
Mukund Rangamani
Keyword(s):  
De Sitter Space ◽  
Field Theories ◽  
Conformal Field Theories ◽  
De Sitter ◽  
Conformal Field

scholarly journals WE PROBABLY LIVE ON AN INFLATING BRANE-WORLD

2011 ◽  
Vol 20 (14) ◽  
pp. 2809-2816
Author(s):  
ISHWAREE P. NEUPANE
Keyword(s):  
Zero Mode ◽  
De Sitter Space ◽  
Brane World ◽  
Conformal Field Theories ◽  
De Sitter ◽  
Conformal Field ◽  
Sitter Spacetime ◽  
Acceleration Of The Universe ◽  
De Sitter Universe ◽  
The Universe

Brane-world models, where observers are trapped within the thickness of a 3-brane, offer novel perspectives on gravitation and cosmology. In this essay, it is argued that the problem of a late epoch acceleration of the universe is well explained in the framework of a 4-dimensional de Sitter universe embedded in a 5-dimensional de Sitter spacetime. While a 5-dimensional Anti-de Sitter space background is important for studying conformal field theories for its role in the AdS/CFT correspondence, the existence of a 5-dimensional de Sitter space is crucial for finding an effective 4-dimensional Newton constant that remains finite and a normalizable zero-mode graviton wave function.

De Sitter and conformal field theories

1982 ◽  
Vol 32 (4) ◽  
pp. 439-471 ◽  
Author(s):  
B. Binegar ◽  
C. Fronsdal ◽  
M. Flato ◽  
S. Salamó
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
De Sitter ◽  
Conformal Field

3D SINGLETONS AND THEIR BOUNDARY 2D CONFORMAL FIELD THEORY

1999 ◽  
Vol 11 (09) ◽  
pp. 1079-1090 ◽  
Author(s):  
SÉBASTIEN MICHÉA
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Recent Work ◽  
De Sitter Space ◽  
Field Theories ◽  
Conformal Field Theories ◽  
De Sitter ◽  
Witt Algebra ◽  
Conformal Field ◽  
De Sitter Universe

This paper is a continuation of recent work of Flato and Frønsdal on singletons in 1+2 anti De Sitter universe and their link with 2D conformal field theories on the boundary. More specifically we show that in this framework we can construct a 3D-singleton model in the bulk, the limit of which on the boundary of De Sitter space is a Gupta–Bleuler triplet for two commuting copies of the Witt algebra. We also generalize this result to the case of WZNW models.

scholarly journals Supercharged AdS3 Holography

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Sami Rawash ◽  
David Turton
Keyword(s):  
De Sitter ◽  
Expectation Values ◽  
Chiral Algebra ◽  
Gauge Invariant ◽  
Conformal Field ◽  
Microscopic Interpretation ◽  
Large Families ◽  
Single Trace ◽  
Holographic Description ◽  
Supergravity Solution

Abstract Given an asymptotically Anti-de Sitter supergravity solution, one can obtain a microscopic interpretation by identifying the corresponding state in the holographically dual conformal field theory. This is of particular importance for heavy pure states that are candidate black hole microstates. Expectation values of light operators in such heavy CFT states are encoded in the asymptotic expansion of the dual bulk configuration. In the D1-D5 system, large families of heavy pure CFT states have been proposed to be holographically dual to smooth horizonless supergravity solutions. We derive the precision holographic dictionary in a new sector of light operators that are superdescendants of scalar chiral primaries of dimension (1,1). These operators involve the action of the supercharges of the chiral algebra, and they play a central role in the proposed holographic description of recently-constructed supergravity solutions known as “supercharged superstrata”. We resolve the mixing of single-trace and multi-trace operators in the CFT to identify the combinations that are dual to single-particle states in the bulk. We identify the corresponding gauge-invariant combinations of supergravity fields. We use this expanded dictionary to probe the proposed holographic description of supercharged superstrata, finding precise agreement between gravity and CFT.

QUASI-EXACTLY-SOLVABLE QUANTAL PROBLEMS: ONE-DIMENSIONAL ANALOGUE OF RATIONAL CONFORMAL FIELD THEORIES

1990 ◽  
Vol 05 (04) ◽  
pp. 803-832 ◽  
Author(s):  
A. YU. MOROZOV ◽  
A.M. PERELOMOV ◽  
A.A. ROSLY ◽  
M.A. SHIFMAN ◽  
A.V. TURBINER
Keyword(s):  
Mathematical Formulation ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Solvable Models ◽  
One Dimensional ◽  
Conformal Field ◽  
Exactly Solvable ◽  
Solvable Problems ◽  
Shed Light ◽  
Ordinary Quantum

The class of quasi-exactly-solvable problems in ordinary quantum mechanics discovered recently shows remarkable parallels with rational two-dimensional conformal field theories. This fact suggests that investigation of the quasi-exactly-solvable models may shed light on rational conformal field theories. We discuss a relation between these two theoretical schemes and propose a mathematical formulation for the procedure of constructing quasi-exactly solvable systems. This discussion leads us to a kind of generalization of the Sugawara construction.

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