scholarly journals Entanglement entropy and edge modes in topological string theory. Part I. Generalized entropy for closed strings

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
William Donnelly ◽  
Yikun Jiang ◽  
Manki Kim ◽  
Gabriel Wong
Keyword(s):  
Hilbert Space ◽  
String Theory ◽  
Entanglement Entropy ◽  
Topological String ◽  
Closed String ◽  
Simons Theory ◽  
Topological String Theory ◽  
Open Strings ◽  
Reduced Density ◽  
Theory Calculation

Abstract Progress in identifying the bulk microstate interpretation of the Ryu-Takayanagi formula requires understanding how to define entanglement entropy in the bulk closed string theory. Unfortunately, entanglement and Hilbert space factorization remains poorly understood in string theory. As a toy model for AdS/CFT, we study the entanglement entropy of closed strings in the topological A-model in the context of Gopakumar-Vafa duality. We will present our results in two separate papers. In this work, we consider the bulk closed string theory on the resolved conifold and give a self-consistent factorization of the closed string Hilbert space using extended TQFT methods. We incorporate our factorization map into a Frobenius algebra describing the fusion and splitting of Calabi-Yau manifolds, and find string edge modes transforming under a q-deformed surface symmetry group. We define a string theory analogue of the Hartle-Hawking state and give a canonical calculation of its entanglement entropy from the reduced density matrix. Our result matches with the geometrical replica trick calculation on the resolved conifold, as well as a dual Chern-Simons theory calculation which will appear in our next paper [1]. We find a realization of the Susskind-Uglum proposal identifying the entanglement entropy of closed strings with the thermal entropy of open strings ending on entanglement branes. We also comment on the BPS microstate counting of the entanglement entropy. Finally we relate the nonlocal aspects of our factorization map to analogous phenomenon recently found in JT gravity.

scholarly journals Entanglement entropy and edge modes in topological string theory. Part II. The dual gauge theory story

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Yikun Jiang ◽  
Manki Kim ◽  
Gabriel Wong
Keyword(s):  
Boundary Condition ◽  
Gauge Theory ◽  
String Theory ◽  
Entanglement Entropy ◽  
Topological String ◽  
Closed String ◽  
Wilson Loops ◽  
Topological String Theory ◽  
Generalized Entropy ◽  
Chern Simons

Abstract This is the second in a two-part paper devoted to studying entanglement entropy and edge modes in the A model topological string theory. This theory enjoys a gauge-string (Gopakumar-Vafa) duality which is a topological analogue of AdS/CFT. In part 1, we defined a notion of generalized entropy for the topological closed string theory on the resolved conifold. We provided a canonical interpretation of the generalized entropy in terms of the q-deformed entanglement entropy of the Hartle-Hawking state. We found string edge modes transforming under a quantum group symmetry and interpreted them as entanglement branes. In this work, we provide the dual Chern-Simons gauge theory description. Using Gopakumar-Vafa duality, we map the closed string theory Hartle-Hawking state to a Chern-Simons theory state containing a superposition of Wilson loops. These Wilson loops are dual to closed string worldsheets that determine the partition function of the resolved conifold. We show that the undeformed entanglement entropy due to cutting these Wilson loops reproduces the bulk generalized entropy and therefore captures the entanglement underlying the bulk spacetime. Finally, we show that under the Gopakumar-Vafa duality, the bulk entanglement branes are mapped to a configuration of topological D-branes, and the non-local entanglement boundary condition in the bulk is mapped to a local boundary condition in the gauge theory dual. This suggests that the geometric transition underlying the gauge-string duality may also be responsible for the emergence of entanglement branes.

scholarly journals Topological holography: The example of the D2-D4 brane system

2020 ◽  
Vol 9 (2) ◽  
Author(s):  
Nafiz Ishtiaque ◽  
Seyed Faroogh Moosavian ◽  
Yehao Zhou
Keyword(s):  
String Theory ◽  
Topological String ◽  
Closed String ◽  
Simons Theory ◽  
Topological String Theory ◽  
One Dimensional ◽  
Bf Theory ◽  
World Volume ◽  
Chern Simons ◽  
Chern Simons Theory

We propose a toy model for holographic duality. The model is constructed by embedding a stack of NN D2-branes and KK D4-branes (with one dimensional intersection) in a 6d topological string theory. The world-volume theory on the D2-branes (resp. D4-branes) is 2d BF theory (resp. 4D Chern-Simons theory) with \mathrm{GL}_NGLN (resp. \mathrm{GL}_KGLK) gauge group. We propose that in the large NN limit the BF theory on \mathbb{R}^2ℝ2 is dual to the closed string theory on \mathbb{R}^2 \times \mathbb{R}_+ \times S^3ℝ2×ℝ+×S3 with the Chern-Simons defect on \mathbb{R} \times \mathbb{R}_+ \times S^2ℝ×ℝ+×S2. As a check for the duality we compute the operator algebra in the BF theory, along the D2-D4 intersection – the algebra is the Yangian of \mathfrak{gl}_K𝔤𝔩K. We then compute the same algebra, in the guise of a scattering algebra, using Witten diagrams in the Chern-Simons theory. Our computations of the algebras are exact (valid at all loops). Finally, we propose a physical string theory construction of this duality using D3-D5 brane configuration in type IIB – using supersymmetric twist and \OmegaΩ-deformation.

scholarly journals Does the HM mechanism work in string theory?

2013 ◽  
Vol 91 (1) ◽  
pp. 75-80
Author(s):  
Alireza Sepehri ◽  
Somayyeh Shoorvazi ◽  
Mohammad Ebrahim Zomorrodian
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
String Theory ◽  
Correspondence Principle ◽  
Black Hole Entropy ◽  
Closed String ◽  
Centre Of Mass ◽  
Final State ◽  
Information Transformation ◽  
Left And Right

The correspondence principle offers a unique opportunity to test the Horowitz and Maldacena mechanism at the correspondence point “the centre of mass energies around (Ms/(gs)2)”. First by using the Horowitz and Maldacena proposal, the black hole final state for closed strings is studied and the entropy of these states is calculated. Then, to consider the closed string states, a copy of the original Hilbert space is constructed with a set of creation–annihilation operators that have the same commutation properties as the original ones. The total Hilbert space is the tensor product of the two spaces Hright ⊗ Hleft, where in this case Hleft/right denote the physical quantum state space of the closed string. It is shown that closed string states can be represented by a maximally entangled two-mode squeezed state of the left and right spaces of closed string. Also, the entropy for these string states is calculated. It is found that black hole entropy matches the closed string entropy at transition point. This means that our result is consistent with correspondence principle and thus HM mechanism in string theory works. Consequently the unitarity of the black hole in string theory can be reconciled. However Gottesman and Preskill point out that, in this scenario, departures from unitarity can arise due to interactions between the collapsing body and the infalling Hawking radiation inside the event horizon and information can be lost. By extending the Gottesman and Preskill method to string theory, the amount of information transformation from the matter to the state of outgoing Hagedorn radiation for closed strings is obtained. It is observed that information is lost for closed strings.

String theory

2018 ◽  
Author(s):  
Ivan Kostov
Keyword(s):  
String Theory ◽  
Matrix Models ◽  
Topological Strings ◽  
Mirror Symmetry ◽  
Topological String ◽  
Enumerative Geometry ◽  
Topological String Theory ◽  
Superstring Theory ◽  
String Dualities ◽  
Supersymmetric Gauge

This article discusses the link between matrix models and string theory, giving emphasis on topological string theory and the Dijkgraaf–Vafa correspondence, along with applications of this correspondence and its generalizations to supersymmetric gauge theory, enumerative geometry, and mirror symmetry. The article first provides an overview of strings and matrices, noting that the correspondence between matrix models and string theory makes it possible to solve both non-critical strings and topological strings. It then describes some basic aspects of topological strings on Calabi-Yau manifolds and states the Dijkgraaf–Vafa correspondence, focusing on how it is connected to string dualities and how it can be used to compute superpotentials in certain supersymmetric gauge theories. In addition, it shows how the correspondence extends to toric manifolds and leads to a matrix model approach to enumerative geometry. Finally, it reviews matrix quantum mechanics and its applications in superstring theory.

scholarly journals Bulk Deformations of Open Topological String Theory

2012 ◽  
Vol 315 (3) ◽  
pp. 739-769
Author(s):  
Nils Carqueville ◽  
Michael M. Kay
Keyword(s):  
String Theory ◽  
Topological String ◽  
Topological String Theory ◽  
Bulk Deformations

scholarly journals Topological entanglement and hyperbolic volume

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Aditya Dwivedi ◽  
Siddharth Dwivedi ◽  
Bhabani Prasad Mandal ◽  
Pichai Ramadevi ◽  
Vivek Kumar Singh
Keyword(s):  
Density Matrix ◽  
Entanglement Entropy ◽  
Reduced Density Matrix ◽  
Simons Theory ◽  
Partition Functions ◽  
Connected Sum ◽  
Gauge Groups ◽  
Hyperbolic Volume ◽  
Reduced Density ◽  
Chern Simons

AbstractThe entanglement entropy of many quantum systems is difficult to compute in general. They are obtained as a limiting case of the Rényi entropy of index m, which captures the higher moments of the reduced density matrix. In this work, we study pure bipartite states associated with S3 complements of a two-component link which is a connected sum of a knot $$ \mathcal{K} $$ K and the Hopf link. For this class of links, the Chern-Simons theory provides the necessary setting to visualise the m-moment of the reduced density matrix as a three-manifold invariant Z($$ {M}_{{\mathcal{K}}_m} $$ M K m ), which is the partition function of $$ {M}_{{\mathcal{K}}_m} $$ M K m . Here $$ {M}_{{\mathcal{K}}_m} $$ M K m is a closed 3-manifold associated with the knot $$ \mathcal{K} $$ K m, where $$ \mathcal{K} $$ K m is a connected sum of m-copies of $$ \mathcal{K} $$ K (i.e., $$ \mathcal{K} $$ K #$$ \mathcal{K} $$ K . . . #$$ \mathcal{K} $$ K ) which mimics the well-known replica method. We analayse the partition functions Z($$ {M}_{{\mathcal{K}}_m} $$ M K m ) for SU(2) and SO(3) gauge groups, in the limit of the large Chern-Simons coupling k. For SU(2) group, we show that Z($$ {M}_{{\mathcal{K}}_m} $$ M K m ) can grow at most polynomially in k. On the contrary, we conjecture that Z($$ {M}_{{\mathcal{K}}_m} $$ M K m ) for SO(3) group shows an exponential growth in k, where the leading term of ln Z($$ {M}_{{\mathcal{K}}_m} $$ M K m ) is the hyperbolic volume of the knot complement S3\$$ \mathcal{K} $$ K m. We further propose that the Rényi entropies associated with SO(3) group converge to a finite value in the large k limit. We present some examples to validate our conjecture and proposal.

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