Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFour-Dimensional Chern-Simons and Gauged Sigma Models
154
0
0.0
(
0
)
Authors
Jake Stedman
Ask ChatGPT about the research
No Arabic abstract
In this paper we introduce a new method for generating gauged sigma models from four-dimensional Chern-Simons theory and give a unified action for a class of these models. We begin with a review of recent work by several authors on the classical generation of integrable sigma models from four dimensional Chern-Simons theory. This approach involves introducing classes of two dimensional defects into the bulk on which the gauge field must satisfy certain boundary conditions. By solving the equations of motion of the gauge one finds an integrable sigma models by substituting the solution back into the action. This integrability is guaranteed because the gauge field is gauge equivalent to the Lax connection of the sigma model. By considering a theory with two four-dimensional Chern-Simons fields coupled together on two dimensional surfaces in the bulk we are able to introduce new classes of `gauged defects. By solving the bulk equations of motion we find a unified action for a set of genus zero integrable gauged sigma models. The integrability of these models is guaranteed as the new coupling does not break the gauge equivalence of the gauged fields to their Lax connections. Finally, we consider a couple of examples in which we derive the gauged Wess-Zumino-Witten and Nilpotent gauged Wess-Zumino-Witten models. This latter model is of note given one can find the conformal Toda models from it.
rate research
Read More
Recently, a variety of deformed $T^{1,1}$ manifolds, with which 2D non-linear sigma models (NLSMs) are classically integrable, have been presented by Arutyunov, Bassi and Lacroix (ABL) [arXiv:2010.05573]. We refer to the NLSMs with the integrable deformed $T^{1,1}$ as the ABL model for brevity. Motivated by this progress, we consider deriving the ABL model from a 4D Chern-Simons (CS) theory with a meromorphic one-form with four double poles and six simple zeros. We specify boundary conditions in the CS theory that give rise to the ABL model and derive the sigma-model background with target-space metric and anti-symmetric two-form. Finally, we present two simple examples 1) an anisotropic $T^{1,1}$ model and 2) a $G/H$ $lambda$-model. The latter one can be seen as a one-parameter deformation of the Guadagnini-Martellini-Mintchev model.
We consider the matrix model of $U(N)$ refined Chern-Simons theory on $S^3$ for the unknot. We derive a $q$-difference operator whose insertion in the matrix integral reproduces an infinite set of Ward identities which we interpret as $q$-Virasoro constraints. The constraints are rewritten as difference equations for the generating function of Wilson loop expectation values which we solve as a recursion for the correlators of the model. The solution is repackaged in the form of superintegrability formulas for Macdonald polynomials. Additionally, we derive an equivalent $q$-difference operator for a similar refinement of ABJ theory and show that the corresponding $q$-Virasoro constraints are equal to those of refined Chern-Simons for a gauge super-group $U(N|M)$. Our equations and solutions are manifestly symmetric under Langlands duality $qleftrightarrow t^{-1}$ which correctly reproduces 3d Seiberg duality when $q$ is a specific root of unity.
We demonstrate generation of the two-dimensional Chern-Simons-like Lorentz-breaking action via an appropriate Lorentz-breaking coupling of scalar and spinor fields at zero as well as at the finite temperature and via the noncommutative fields method and study the dispersion relations corresponding to this action.
We describe supersymmetric A-branes and B-branes in open N=(2,2) dynamically gauged nonlinear sigma models (GNLSM), placing emphasis on toric manifold target spaces. For a subset of toric manifolds, these equivariant branes have a mirror description as branes in gauged Landau-Ginzburg models with neutral matter. We then study correlation functions in the topological A-twisted version of the GNLSM, and identify their values with open Hamiltonian Gromov-Witten invariants. Supersymmetry breaking can occur in the A-twisted GNLSM due to nonperturbative open symplectic vortices, and we canonically BRST quantize the mirror theory to analyze this phenomenon.
Kronheimer and Mrowka asked whether the difference between the four-dimensional clasp number and the slice genus can be arbitrarily large. This question is answered affirmatively by studying a knot invariant derived from equivariant singular instanton theory, and which is closely related to the Chern--Simons functional. This also answers a conjecture of Livingston about slicing numbers. Also studied is the singular instanton Fr{o}yshov invariant of a knot. If defined with integer coefficients, this gives a lower bound for the unoriented slice genus, and is computed for quasi-alternating and torus knots. In contrast, for certain other coefficient rings, the invariant is identified with a multiple of the knot signature. This result is used to address a conjecture by Poudel and Saveliev about traceless $SU(2)$ representations of torus knots. Further, for a concordance between knots with non-zero signature, it is shown that there is a traceless representation of the concordance complement which restricts to non-trivial representations of the knot groups. Finally, some evidence towards an extension of the slice-ribbon conjecture to torus knots is provided.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
