scholarly journals Supersymmetric solitons and a degeneracy of solutions in AdS/CFT

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Andrés Anabalón ◽  
Simon F. Ross
Keyword(s):  
Phase Transition ◽  
Riemann Surface ◽  
Magnetic Flux ◽  
Gauge Field ◽  
Wilson Line ◽  
Saddle Points ◽  
Planar Boundary ◽  
Four Dimensions ◽  
Special Value

Abstract We study Lorentzian supersymmetric configurations in D = 4 and D = 5 gauged $$ \mathcal{N} $$ N = 2 supergravity. We show that there are smooth 1/2 BPS solutions which are asymptotically AdS4 and AdS5 with a planar boundary, a compact spacelike direction and with a Wilson line on that circle. There are solitons where the S1 shrinks smoothly to zero in the interior, with a magnetic flux through the circle determined by the Wilson line, which are AdS analogues of the Melvin fluxtube. There is also a solution with a constant gauge field, which is pure AdS. Both solutions preserve half of the supersymmetries at a special value of the Wilson line. There is a phase transition between these two saddle-points as a function of the Wilson line precisely at the supersymmetric point. Thus, the supersymmetric solutions are degenerate, at least at the supergravity level. We extend this discussion to one of the Romans solutions in four dimensions when the Euclidean boundary is S1× Σg where Σg is a Riemann surface with genus g > 0. We speculate that the supersymmetric state of the CFT on the boundary is dual to a superposition of the two degenerate geometries.

scholarly journals Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Gauge Field ◽  
Wilson Line ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

scholarly journals Magnetic flux, Wilson line, and orbifold

2009 ◽  
Vol 80 (12) ◽  
Author(s):  
Hiroyuki Abe ◽  
Kang-Sin Choi ◽  
Tatsuo Kobayashi ◽  
Hiroshi Ohki
Keyword(s):  
Magnetic Flux ◽  
Wilson Line

scholarly journals Residues and Topological Yang–Mills Theory in Two Dimensions

1997 ◽  
Vol 09 (01) ◽  
pp. 59-75
Author(s):  
Kenji Mohri
Keyword(s):  
Correlation Function ◽  
Riemann Surface ◽  
Magnetic Flux ◽  
Recursion Relation ◽  
Two Dimensions ◽  
Yang Mills ◽  
Residue Formula ◽  
Valued Field ◽  
Physical Quantities

A residue formula which evaluates any correlation function of topological SUn Yang–Mills theory with arbitrary magnetic flux insertion in two-dimensions are obtained. Deformations of the system by two-form operators are investigated in some detail. The method of the diagonalization of a matrix-valued field turns out to be useful to compute various physical quantities. As an application we find the operator that contracts a handle of a Riemann surface and a genus recursion relation.

scholarly journals General Relativity with a Positive Cosmological Constant Λ as a Gauge Theory

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 24
Author(s):  
Marta Dudek ◽  
Janusz Garecki
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Cosmological Constant ◽  
Gauge Field ◽  
Geometrical Interpretation ◽  
Positive Cosmological Constant ◽  
Four Dimensions ◽  
Action Integral ◽  
Fields Equations

In this paper, we show that the general relativity action (and Lagrangian) in recent Einstein–Palatini formulation is equivalent in four dimensions to the action (and Langrangian) of a gauge field. First, we briefly showcase the Einstein–Palatini (EP) action, and then we present how Einstein fields equations can be derived from it. In the next section, we study Einstein–Palatini action integral for general relativity with a positive cosmological constant Λ in terms of the corrected curvature Ω c o r . We see that in terms of Ω c o r this action takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the corrected curvature Ω c o r .

scholarly journals Consistent Interactions in Terms of the Generalized Fields Method

1997 ◽  
Vol 12 (24) ◽  
pp. 4387-4397 ◽  
Author(s):  
Ömer F. Dayi
Keyword(s):  
Master Equation ◽  
Gauge Field ◽  
Tensor Field ◽  
General Scheme ◽  
Antisymmetric Tensor ◽  
Four Dimensions ◽  
Bf Theory ◽  
Free Theory ◽  
Antisymmetric Tensor Field

The interactions which preserve the structure of the gauge interactions of the free theory are introduced in terms of the generalized fields method for solving the Batalin–Vilkovisky master equation. It is shown that by virtue of this method the solution of the descent equations resulting from the cohomological analysis is provided straightforwardly. The general scheme is illustrated by applying it to the spin 1 gauge field in three and four dimensions, to free BF theory in 2D, and to the antisymmetric tensor field in any dimension. It is shown that it reproduces the results obtained by cohomological techniques.

Design of magneto-optical system for imaging of magnetic flux created during a conductor–superconductor phase transition

2008 ◽  
Vol 366 (1877) ◽  
pp. 2843-2849 ◽  
Author(s):  
Daniel Golubchik ◽  
Emil Polturak ◽  
Gad Koren
Keyword(s):  
Phase Transition ◽  
Magnetic Flux ◽  
Optical System ◽  
Flux Line ◽  
Spatial Density ◽  
Flux Lines

According to the Kibble–Zurek model, flux lines are spontaneously created during a fast conductor–superconductor phase transition. The model predicts both the spatial density and the correlations of the flux array. We present the design of a magneto-optical system with a projected single-flux-line resolution. Such a system can allow detailed measurements of the distribution of flux created spontaneously during a conductor–superconductor phase transition.

A Concurrent Search Algorithm for Multiple Phase Transition Pathways

2013 ◽  
Author(s):  
Lijuan He ◽  
Yan Wang
Keyword(s):  
Phase Transition ◽  
Search Algorithm ◽  
Minimum Energy ◽  
Saddle Points ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Conjugate Directions ◽  
Control Points ◽  
True Value ◽  
Transition Paths

The challenge of accurately predicting a phase transition in computer-aided nano-design is estimating the true value of transition rate, which is determined by the saddle point with the minimum energy barrier between stable states on the potential energy surface (PES). In this paper, a new algorithm for searching the minimum energy path (MEP) is presented. Unlike existing pathway search methods, the new algorithm is able to locate both the saddle points and local minima simultaneously. Therefore no prior knowledge of the precise positions for the reactant and product on the PES is required. In addition, the algorithm is able to search multiple transition paths on the PES simultaneously. In this method, a Bézier curve is used to represent each transition path. Starting from a single Bézier curve, multiple curves with ends connected can be generated during the search process. For each Bézier curve, the reactant and product states are located by minimizing the two end control points of the curve, while the transition pathway is refined by moving the intermediate control points of the curve in the conjugate directions. A curve subdivision scheme is developed so that multiple transition paths can be located. The algorithm is demonstrated by examples.

scholarly journals MULTIPLE CHERN–SIMONS FIELDS ON A TORUS

1994 ◽  
Vol 09 (06) ◽  
pp. 969-989 ◽  
Author(s):  
DENNE WESOLOWSKI ◽  
YUTAKA HOSOTANI ◽  
CHOON-LIN HO
Keyword(s):  
Hilbert Space ◽  
Gauge Field ◽  
Wilson Line ◽  
Wave Functions ◽  
Effective Theory ◽  
Gauge Fields ◽  
Vacuum Structure ◽  
Vacuum Degeneracy ◽  
Chern Simons

Intertwined multiple Chern–Simons gauge fields induce matrix statistics among particles. We analyze this theory on a torus, focusing on the vacuum structure and the Hilbert space. The theory can be mimicked, although not completely, by an effective theory with one Chern–Simons gauge field. The correspondence between the Wilson line integrals, vacuum degeneracy and wave functions for these two theories are discussed. Further, it is found in both of these cases that the two total momenta and Hamiltonian commute only in the physical Hilbert space.

Sign in / Sign up

Export Citation Format

Share Document