scholarly journals On recursion relations in topological string theory

2013 ◽  
Vol 2013 (2) ◽  
Author(s):  
Andrea Prudenziati
Keyword(s):  
String Theory ◽  
Topological String ◽  
Topological String Theory ◽  
Recursion Relations

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 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 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.

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