scholarly journals D-branes in AdS3 × S3 × 𝕋4 at k = 1 and their holographic duals

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Matthias R. Gaberdiel ◽  
Bob Knighton ◽  
Jakub Vošmera
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Moduli Space ◽  
Free Field ◽  
Boundary States ◽  
Holographic Duals ◽  
Direct Correspondence

Abstract String theory on AdS3× S3× 𝕋4 with minimal k = 1 NS-NS flux can be described in terms of a free field worldsheet theory in the hybrid formalism. We construct various D-branes of this string theory and calculate their associated cylinder amplitudes. We find that these amplitudes match with the cylinder correlators of certain boundary states of the dual symmetric orbifold CFT Sym(𝕋4), thus suggesting a direct correspondence between these boundary conditions. We also show that the disk amplitudes of these D-branes localise to those points in the worldsheet moduli space where the worldsheet disk holomorphically covers the spacetime disk.

scholarly journals Higher genus correlators for tensionless AdS3 strings

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Bob Knighton
Keyword(s):  
Perturbation Theory ◽  
String Theory ◽  
Moduli Space ◽  
Strong Evidence ◽  
Correlation Functions ◽  
Free Field ◽  
Tree Level ◽  
Branched Covering ◽  
Free Field Realization ◽  
Higher Genus

Abstract It was recently shown in [1] that tree-level correlation functions in tensionless string theory on AdS3 × S3 × $$ {\mathbbm{T}}^4 $$ T 4 match the expected form of correlation functions in the symmetric orbifold CFT on $$ {\mathbbm{T}}^4 $$ T 4 in the large N limit. This analysis utilized the free-field realization of the $$ \mathfrak{psu}{\left(1,\left.1\right|2\right)}_1 $$ psu 1 1 2 1 Wess-Zumino-Witten model, along with a surprising identity directly relating these correlation functions to a branched covering of the boundary of AdS3. In particular, this identity implied the unusual feature that the string theory correlators localize to points in the moduli space for which the worldsheet covers the boundary of AdS3 with specified branching near the insertion points. In this work we generalize this analysis past the tree-level approximation, demonstrating its validity to higher genus worldsheets, and in turn providing strong evidence for this incarnation of the AdS/CFT correspondence at all orders in perturbation theory.

scholarly journals Singular BPS boundary conditions in $$ \mathcal{N} $$ = (2, 2) supersymmetric gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Tadashi Okazaki ◽  
Douglas J. Smith
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Gauge Theories ◽  
Holomorphic Curve ◽  
Two Dimensional ◽  
Supersymmetric Gauge Theories ◽  
Special Lagrangian ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract We derive general BPS boundary conditions in two-dimensional $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow the bulk fields to have poles at the boundary. We also present the brane configurations for the half- and quarter-BPS boundary conditions of the $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories in terms of branes in Type IIA string theory. We find that both A-type and B-type brane configurations are lifted to M-theory as a system of M2-branes ending on an M5-brane wrapped on a product of a holomorphic curve in ℂ2 with a special Lagrangian 3-cycle in ℂ3.

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 Boundary states for chiral symmetries in two dimensions

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Philip Boyle Smith ◽  
David Tong
Keyword(s):  
Boundary Conditions ◽  
Ground State ◽  
Zero Mode ◽  
Central Charge ◽  
Two Dimensions ◽  
Dirac Fermions ◽  
Chiral Symmetries ◽  
Boundary States ◽  
Ground State Degeneracy ◽  
Left And Right

Abstract We study boundary states for Dirac fermions in d = 1 + 1 dimensions that preserve Abelian chiral symmetries, meaning that the left- and right-moving fermions carry different charges. We derive simple expressions, in terms of the fermion charge assignments, for the boundary central charge and for the ground state degeneracy of the system when two different boundary conditions are imposed at either end of an interval. We show that all such boundary states fall into one of two classes, related to SPT phases supported by (−1)F , which are characterised by the existence of an unpaired Majorana zero mode.

CHIRAL ZEROMODES ON VORTEX-TYPE INTERSECTING FIVE-BRANE IN HETEROTIC STRING

2013 ◽  
Vol 21 ◽  
pp. 191-192
Author(s):  
MASAYA YATA
Keyword(s):  
Dirac Equation ◽  
String Theory ◽  
Boundary Conditions ◽  
Heterotic String ◽  
The Other ◽  
Two Dimensional ◽  
Complete Spectrum ◽  
Heterotic String Theory ◽  
Brane Solution ◽  
Opposite Chirality

We solve the gaugino Dirac equation on a smeared intersecting five-brane solution in E8 × E8 heterotic string theory to search for localized chiral zeromodes on the intersection. The background is chosen to depend on the full two-dimensional overall transverse coordinates to the branes. Under some appropriate boundary conditions, we compute the complete spectrum of zeromodes to find that, among infinite towers of Fourier modes, there exist only three localized normalizable zeromodes, one of which has opposite chirality to the other two.

scholarly journals Calabi-Yau moduli space, mirror manifolds and spacetime topology change in string theory

1994 ◽  
Vol 416 (2) ◽  
pp. 414-480 ◽  
Author(s):  
Paul S. Aspinwall ◽  
Brian R. Greene ◽  
David R. Morrison
Keyword(s):  
String Theory ◽  
Moduli Space ◽  
Topology Change ◽  
Spacetime Topology

scholarly journals SUPERPOTENTIAL OF THE M-THEORY CONIFOLD AND TYPE IIA STRING THEORY

2004 ◽  
Vol 19 (04) ◽  
pp. 521-555 ◽  
Author(s):  
GOTTFRIED CURIO
Keyword(s):  
String Theory ◽  
Heisenberg Group ◽  
Group Action ◽  
Moduli Space ◽  
Monodromy Group ◽  
Witten Theory ◽  
Flat Bundle ◽  
M Theory

The membrane instanton superpotential for M-theory on the G2 holonomy manifold given by the cone on S3×S3 is given by the dilogarithm and has Heisenberg monodromy group in the quantum moduli space. We compare this to a Heisenberg group action on the type IIA hypermultiplet moduli space for the universal hypermultiplet, to metric corrections from membrane instantons related to a twisted dilogarithm for the deformed conifold and to a flat bundle related to a conifold period, the Heisenberg group and the dilogarithm appearing in five-dimensional Seiberg/Witten theory.

scholarly journals THE ENHANÇON, MULTIMONOPOLES AND FUZZY GEOMETRY

2001 ◽  
Vol 16 (05) ◽  
pp. 990-1001 ◽  
Author(s):  
CLIFFORD V. JOHNSON
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Moduli Space ◽  
Fuzzy Sphere ◽  
Fuzzy Geometry ◽  
Space Geometry ◽  
The Difference ◽  
A Charge ◽  
Insight Into

The presentation at Strings 2000 was intended to be in two main parts, but there was only time for part one. However both parts appeared on the online proceedings, and are also included in this document. The first part concerns an exploration of the connection between the physics of the "enhançon" geometry arising from wrapping N D6–branes on the K3 manifold in Type IIA string theory and that of a charge N BPS multi–monopole. This also relates to the physics of 2+1 dimensional SU(N) gauge theory with eight supercharges. The main results uncovered by this exploration are: a) better insight into the non–perturbative geometry of the enhançon; b) the structure of the moduli space geometry, and its characterisation in terms of a family of Atiyah–Hitchin–like manifolds; c) the use of Nahm data to describe aspects of the geometry, showing that the enhançon locus itself has a description as a fuzzy sphere. Part two discusses the addition of extra D2–branes into the geometry. Two probe computations show the difference between the geometry as seen by D2–branes and that seen by wrapped D6–branes, and the accompanying gauge theory interpretations are discussed.

scholarly journals A NOTE ON KERR/CFT AND FREE FIELDS

2010 ◽  
Vol 25 (20) ◽  
pp. 3965-3973 ◽  
Author(s):  
JØRGEN RASMUSSEN
Keyword(s):  
Black Hole ◽  
Boundary Conditions ◽  
Isometry Group ◽  
Free Field ◽  
Kerr Black Hole ◽  
Virasoro Algebra ◽  
Free Fields ◽  
Horizon Geometry

The near-horizon geometry of the extremal four-dimensional Kerr black hole and certain generalizations thereof has an SL (2, ℝ) × U (1) isometry group. Excitations around this geometry can be controlled by imposing appropriate boundary conditions. For certain boundary conditions, the U(1) isometry is enhanced to a Virasoro algebra. Here, we propose a free-field construction of this Virasoro algebra.

scholarly journals A MPM framework for large deformation seismic response analysis

2021 ◽  
Author(s):  
Marc Kohler ◽  
Andreas Stoecklin ◽  
Alexander M. Puzrin
Keyword(s):  
Boundary Conditions ◽  
Seismic Response ◽  
Large Deformation ◽  
Free Field ◽  
Large Mass ◽  
Material Point ◽  
Ground Movement ◽  
Response Analysis ◽  
Seismic Response Analysis ◽  
Seismic Triggering

Landslides are often triggered by earthquakes and can cause immense damage due to large mass movements. To model such large-deformation events, the material point method (MPM) has become increasingly popular in recent years. A limitation of existing MPM implementations is the lack of appropriate boundary conditions to perform seismic response analysis of slopes. In this article, an extension to the basic MPM framework is proposed for simulating the seismic triggering and subsequent collapse of slopes within a single analysis step. Original implementations of a compliant base boundary and free-field boundary conditions in the MPM framework are presented, enabling the application of input ground motions while accounting for the absorption of outgoing waves and the free-ground movement at the lateral boundaries. An example slope is analysed to illustrate the proposed procedure and to benchmark it against the results obtained using an independent simulation technique, based on a three-step FE analysis. The comparison generally shows a good agreement of the results obtained from the two independent procedures and highlights advantages of the presented “all-in-one” MPM approach, in particular for long duration strong motions.

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