scholarly journals Chern-Simons theory on spherical Seifert manifolds, topological strings and integrable systems

2018 ◽  
Vol 22 (2) ◽  
pp. 305-394 ◽  
Author(s):  
Gaëtan Borot ◽  
Andrea Brini
Keyword(s):  
Topological Strings ◽  
Integrable Systems ◽  
Simons Theory ◽  
Seifert Manifolds ◽  
Chern Simons ◽  
Chern Simons Theory

scholarly journals On partition functions of refined Chern-Simons theories on S3

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
M.Y. Avetisyan ◽  
R.L. Mkrtchyan
Keyword(s):  
Partition Function ◽  
Gauge Group ◽  
Topological Strings ◽  
Simons Theory ◽  
Partition Functions ◽  
Coupling Constant ◽  
Sine Functions ◽  
Chern Simons ◽  
Arbitrary Gauge ◽  
Chern Simons Theory

Abstract We present a new expression for the partition function of the refined Chern-Simons theory on S3 with an arbitrary gauge group, which is explicitly equal to 1 when the coupling constant is zero. Using this form of the partition function we show that the previously known Krefl-Schwarz representation of the partition function of the refined Chern-Simons theory on S3 can be generalized to all simply laced algebras.For all non-simply laced gauge algebras, we derive similar representations of that partition function, which makes it possible to transform it into a product of multiple sine functions aiming at the further establishment of duality with the refined topological strings.

scholarly journals Deformation of surfaces, integrable systems, and Chern–Simons theory

2001 ◽  
Vol 42 (3) ◽  
pp. 1397 ◽  
Author(s):  
L. Martina ◽  
Kur. Myrzakul ◽  
R. Myrzakulov ◽  
G. Soliani
Keyword(s):  
Integrable Systems ◽  
Simons Theory ◽  
Chern Simons ◽  
Chern Simons Theory

scholarly journals Topological strings, two-dimensional Yang-Mills theory and Chern-Simons theory on torus bundles

2008 ◽  
Vol 12 (5) ◽  
pp. 981-1058 ◽  
Author(s):  
Nicola Caporaso ◽  
Michele Cirafici ◽  
Luca Griguolo ◽  
Sara Pasquetti ◽  
Domenico Seminara ◽  
...  
Keyword(s):  
Topological Strings ◽  
Simons Theory ◽  
Two Dimensional ◽  
Yang Mills ◽  
Torus Bundles ◽  
Chern Simons ◽  
Chern Simons Theory

scholarly journals Resurgent analysis for some 3-manifold invariants

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Hee-Joong Chung
Keyword(s):  
Partition Function ◽  
Jones Polynomial ◽  
Infinite Family ◽  
Simons Theory ◽  
Flat Connections ◽  
Torus Knot ◽  
Seifert Manifolds ◽  
Resurgent Analysis ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We study resurgence for some 3-manifold invariants when Gℂ = SL(2, ℂ). We discuss the case of an infinite family of Seifert manifolds for general roots of unity and the case of the torus knot complement in S3. Via resurgent analysis, we see that the contribution from the abelian flat connections to the analytically continued Chern-Simons partition function contains the information of all non-abelian flat connections, so it can be regarded as a full partition function of the analytically continued Chern-Simons theory on 3-manifolds M3. In particular, this directly indicates that the homological block for the torus knot complement in S3 is an analytic continuation of the full G = SU(2) partition function, i.e. the colored Jones polynomial.

REDUCTIONS OF CHERN–SIMONS THEORY RELATED TO INTEGRABLE SYSTEMS WHICH HAVE GEOMETRIC APPLICATIONS

2004 ◽  
Vol 18 (09) ◽  
pp. 1261-1275 ◽  
Author(s):  
PAUL BRACKEN
Keyword(s):  
Integrable Systems ◽  
Equations Of Motion ◽  
Moving Frame ◽  
Simons Theory ◽  
Gauge Potential ◽  
Pure Gauge ◽  
Zero Curvature ◽  
Lagrangian Form ◽  
Chern Simons ◽  
Chern Simons Theory

The Chern–Simons functional is introduced in terms of chiral fields and then studied here. The current can be regarded as a non-Abelian pure gauge potential so that the zero-curvature equations are of Lagrangian form for pure non-Abelian Chern–Simons theory. The equations of motion are developed and a formalism which connects the zero curvature equations with a related moving trihedral is introduced. The moving frame equations are written down for the system and a correspondence between these equations and several related elementary integrable systems is described in the same formalism as well.

scholarly journals Twistor Actions for Integrable Systems

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Robert F. Penna
Keyword(s):  
Integrable Systems ◽  
Dimensional Reduction ◽  
Vector Bundles ◽  
Sigma Model ◽  
Twistor Space ◽  
Equations Of Motion ◽  
Simons Theory ◽  
Holomorphic Vector Bundles ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract Many integrable systems can be reformulated as holomorphic vector bundles on twistor space. This is a powerful organizing principle in the theory of integrable systems. One shortcoming is that it is formulated at the level of the equations of motion. From this perspective, it is mysterious that integrable systems have Lagrangians. In this paper, we study a Chern-Simons action on twistor space and use it to derive the Lagrangians of some integrable sigma models. Our focus is on examples that come from dimensionally reduced gravity and supergravity. The dimensional reduction of general relativity to two spacetime dimensions is an integrable coset sigma model coupled to a dilaton and 2d gravity. The dimensional reduction of supergravity to two spacetime dimensions is an integrable coset sigma model coupled to matter fermions, a dilaton, and 2d supergravity. We derive Lax operators and Lagrangians for these 2d integrable systems using the Chern-Simons theory on twistor space. In the supergravity example, we use an extended setup in which twistor Chern-Simons theory is coupled to a pair of matter fermions.

Chern-Simons theory for electrons in high Landau levels

1999 ◽  
Vol 09 (PR10) ◽  
pp. Pr10-223-Pr10-225
Author(s):  
S. Scheidl ◽  
B. Rosenow
Keyword(s):  
Landau Levels ◽  
Simons Theory ◽  
Chern Simons ◽  
Chern Simons Theory
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