scholarly journals SCALING LIMITS OF THE CHERN–SIMONS–HIGGS ENERGY

2008 ◽  
Vol 10 (01) ◽  
pp. 1-16 ◽  
Author(s):  
MATTHIAS KURZKE ◽  
DANIEL SPIRN
Keyword(s):  
The Self ◽  
Scaling Limits ◽  
Gamma Convergence ◽  
Two Dimensional ◽  
Energy Formula ◽  
Simply Connected ◽  
Weak Topologies ◽  
Chern Simons ◽  
Dual Case ◽  
Dimensional Domain

We continue our study in [16] of the Gamma limit of the Abelian Chern–Simons–Higgs energy [Formula: see text] on a bounded, simply connected, two-dimensional domain where ε → 0 and με → μ ∈ [0, +∞]. Under the critical scaling, Gcsh ≈ | log ε2, we establish the Gamma limit when μ ∈ (0,+∞], and as a consequence, we are able to compute the first critical field H1 = H1(U,μ) for the nucleation of a vortex. Finally, we show failure of Gamma convergence when μμ → 0 (this includes the self-dual case). The method entails estimating in certain weak topologies the Jacobian J(uε) = det (∇ uε) in terms of the Chern–Simons–Higgs energy Ecsh.

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 Circular quiver gauge theories, isomonodromic deformations and $$W_N$$ fermions on the torus

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Fabrizio Del Monte ◽  
Pavlo Gavrylenko ◽  
Alessandro Tanzini
Keyword(s):  
Integrable System ◽  
Gauge Theories ◽  
The Self ◽  
Free Fermion ◽  
Two Dimensional ◽  
Isomonodromic Deformation ◽  
Specific Time ◽  
Dimensional Torus ◽  
Isomonodromic Deformations ◽  
Deformation Problem

AbstractWe study the relation between class $$\mathcal {S}$$ S theories on punctured tori and isomonodromic deformations of flat SL(N) connections on the two-dimensional torus with punctures. Turning on the self-dual $$\Omega $$ Ω -background corresponds to a deautonomization of the Seiberg–Witten integrable system which implies a specific time dependence in its Hamiltonians. We show that the corresponding $$\tau $$ τ -function is proportional to the dual gauge theory partition function, the proportionality factor being a nontrivial function of the solution of the deautonomized Seiberg–Witten integrable system. This is obtained by mapping the isomonodromic deformation problem to $$W_N$$ W N free fermion correlators on the torus.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

PSS Business Case Map: Supporting Idea Generation in PSS Design

2012 ◽  
Author(s):  
Fumiya Akasaka ◽  
Kazuki Fujita ◽  
Yoshiki Shimomura
Keyword(s):  
Idea Generation ◽  
Business Case ◽  
Literature Survey ◽  
The Self ◽  
High Dimensional ◽  
Self Organizing Map ◽  
Two Dimensional ◽  
Service Type ◽  
Business Cases ◽  
Low Dimensional

This paper proposes the PSS Business Case Map as a tool to support designers’ idea generation in PSS design. The map visualizes the similarities among PSS business cases in a two-dimensional diagram. To make the map, PSS business cases are first collected by conducting, for example, a literature survey. The collected business cases are then classified from multiple aspects that characterize each case such as its product type, service type, target customer, and so on. Based on the results of this classification, the similarities among the cases are calculated and visualized by using the Self-Organizing Map (SOM) technique. A SOM is a type of artificial neural network that is trained using unsupervised learning to produce a low-dimensional (typically two-dimensional) view from high-dimensional data. The visualization result is offered to designers in a form of a two-dimensional map, which is called the PSS Business Case Map. By using the map, designers can figure out the position of their current business and can acquire ideas for the servitization of their business.

EQUIVALENCE OF TWO-DIMENSIONAL GRAVITIES

1990 ◽  
Vol 05 (16) ◽  
pp. 1251-1258 ◽  
Author(s):  
NOUREDDINE MOHAMMEDI
Keyword(s):  
Gauge Theory ◽  
Explicit Solution ◽  
Light Cone ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Dimensional Gravity ◽  
The Relationship ◽  
Chern Simons

We find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL (2, R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2+1 dimensional gravity. We present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given.

Sign in / Sign up

Export Citation Format

Share Document