scholarly journals Integrable deformed T1,1 sigma models from 4D Chern-Simons theory

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Osamu Fukushima ◽  
Jun-ichi Sakamoto ◽  
Kentaroh Yoshida
Keyword(s):  
Boundary Conditions ◽  
Sigma Models ◽  
Sigma Model ◽  
Target Space ◽  
Simons Theory ◽  
Non Linear ◽  
Linear Sigma Models ◽  
Chern Simons ◽  
Parameter Deformation ◽  
Chern Simons Theory

Abstract Recently, a variety of deformed T1,1 manifolds, with which 2D non-linear sigma models (NLSMs) are classically integrable, have been presented by Arutyunov, Bassi and Lacroix (ABL) [46]. We refer to the NLSMs with the integrable deformed T1,1 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 T1,1 model and 2) a G/H λ-model. The latter one can be seen as a one-parameter deformation of the Guadagnini-Martellini-Mintchev model.

scholarly journals Yang-Baxter deformations of the AdS5×S5 supercoset sigma model from 4D Chern-Simons theory

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Osamu Fukushima ◽  
Jun-ichi Sakamoto ◽  
Kentaroh Yoshida
Keyword(s):  
Boundary Conditions ◽  
Sigma Model ◽  
Simons Theory ◽  
Chiral Model ◽  
Model Case ◽  
Principal Chiral Model ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We present homogeneous Yang-Baxter deformations of the AdS5×S5 supercoset sigma model as boundary conditions of a 4D Chern-Simons theory. We first generalize the procedure for the 2D principal chiral model developed by Delduc et al. [5] so as to reproduce the 2D symmetric coset sigma model, and specify boundary conditions governing homogeneous Yang-Baxter deformations. Then the conditions are applicable for the AdS5×S5 supercoset sigma model case as well. In addition, homogeneous bi-Yang-Baxter deformation is also discussed.

scholarly journals The Geometry of the Master Equation and Topological Quantum Field Theory

1997 ◽  
Vol 12 (07) ◽  
pp. 1405-1429 ◽  
Author(s):  
M. Alexandrov ◽  
A. Schwarz ◽  
O. Zaboronsky ◽  
M. Kontsevich
Keyword(s):  
Master Equation ◽  
Sigma Model ◽  
Target Space ◽  
Simons Theory ◽  
Quantum Field ◽  
Geometric Constructions ◽  
Topological Quantum ◽  
Chern Simons ◽  
Natural Way ◽  
Chern Simons Theory

In Batalin–Vilkovisky formalism, a classical mechanical system is specified by means of a solution to the classical master equation. Geometrically, such a solution can be considered as a QP-manifold, i.e. a supermanifold equipped with an odd vector field Q obeying {Q, Q} = 0 and with Q-invariant odd symplectic structure. We study geometry of QP-manifolds. In particular, we describe some construction of QP-manifolds and prove a classification theorem (under certain conditions). We apply these geometric constructions to obtain in a natural way the action functionals of two-dimensional topological sigma-models and to show that the Chern–Simons theory in BV-formalism arises as a sigma-model with target space [Formula: see text]. (Here [Formula: see text] stands for a Lie algebra and Π denotes parity inversion.)

scholarly journals ON CANONICAL QUANTIZATION OF THE GAUGED WZW MODEL WITH PERMUTATION BRANES

2011 ◽  
Vol 26 (26) ◽  
pp. 4647-4660
Author(s):  
GOR SARKISSIAN
Keyword(s):  
Riemann Surface ◽  
Phase Space ◽  
Boundary Conditions ◽  
Canonical Quantization ◽  
Simons Theory ◽  
Gauge Fields ◽  
Time Line ◽  
Chern Simons ◽  
Special Case ◽  
Chern Simons Theory

In this paper we perform canonical quantization of the product of the gauged WZW models on a strip with boundary conditions specified by permutation branes. We show that the phase space of the N-fold product of the gauged WZW model G/H on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of the double Chern–Simons theory on a sphere with N holes times the time-line with G and H gauge fields both coupled to two Wilson lines. For the special case of the topological coset G/G we arrive at the conclusion that the phase space of the N-fold product of the topological coset G/G on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of Chern–Simons theory on a Riemann surface of the genus N-1 times the time-line with four Wilson lines.

scholarly journals 4d Chern-Simons theory as a 3d Toda theory, and a 3d-2d correspondence

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Meer Ashwinkumar ◽  
Kee-Seng Png ◽  
Meng-Chwan Tan
Keyword(s):  
Moduli Space ◽  
Sigma Model ◽  
Three Dimensional ◽  
Simons Theory ◽  
Yang Mills ◽  
Pole Type ◽  
Type Boundary ◽  
Chern Simons ◽  
Manifold With Corners ◽  
Chern Simons Theory

Abstract We show that the four-dimensional Chern-Simons theory studied by Costello, Witten and Yamazaki, is, with Nahm pole-type boundary conditions, dual to a boundary theory that is a three-dimensional analogue of Toda theory with a novel 3d W-algebra symmetry. By embedding four-dimensional Chern-Simons theory in a partial twist of the five-dimensional maximally supersymmetric Yang-Mills theory on a manifold with corners, we argue that this three-dimensional Toda theory is dual to a two-dimensional topological sigma model with A-branes on the moduli space of solutions to the Bogomolny equations. This furnishes a novel 3d-2d correspondence, which, among other mathematical implications, also reveals that modules of the 3d W-algebra are modules for the quantized algebra of certain holomorphic functions on the Bogomolny moduli space.

scholarly journals Gravitational dual of averaged free CFT’s over the Narain lattice

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Alfredo Pérez ◽  
Ricardo Troncoso
Keyword(s):  
Partition Function ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Simons Theory ◽  
Energy Tensor ◽  
The Family ◽  
Stress Energy ◽  
Higher Spin ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract It has been recently argued that the averaging of free CFT’s over the Narain lattice can be holographically described through a Chern-Simons theory for U (1)D×U (1)D with a precise prescription to sum over three-dimensional handlebodies. We show that a gravitational dual of these averaged CFT’s would be provided by Einstein gravity on AdS3 with U (1)D−1× U (1)D−1 gauge fields, endowed with a precise set of boundary conditions closely related to the “soft hairy” ones. Gravitational excitations then go along diagonal SL (2, ℝ) generators, so that the asymptotic symmetries are spanned by U (1)D× U (1)D currents. The stress-energy tensor can then be geometrically seen as composite of these currents through a twisted Sugawara construction. Our boundary conditions are such that for the reduced phase space, there is a one-to-one map between the configurations in the gravitational and the purely abelian theories. The partition function in the bulk could then also be performed either from a non-abelian Chern-Simons theory for two copies of SL (2, ℝ) × U (1)D−1 generators, or formally through a path integral along the family of allowed configurations for the metric. The new boundary conditions naturally accommodate BTZ black holes, and the microscopic number of states then appears to be manifestly positive and suitably accounted for from the partition function in the bulk. The inclusion of higher spin currents through an extended twisted Sugawara construction in the context of higher spin gravity is also briefly addressed.

The solution structure of the O(3) sigma model in a Maxwell-Chern-Simons theory

2017 ◽  
Vol 58 (7) ◽  
pp. 071503 ◽  
Author(s):  
Sze-Guang Yang ◽  
Zhi-You Chen ◽  
Jann-Long Chern
Keyword(s):  
Solution Structure ◽  
Sigma Model ◽  
Simons Theory ◽  
Chern Simons ◽  
Chern Simons Theory

scholarly journals Symmetric space λ-model exchange algebra from 4d holomorphic Chern-Simons theory

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
David M. Schmidtt
Keyword(s):  
Symmetric Space ◽  
Sigma Model ◽  
Hamiltonian Formalism ◽  
Simons Theory ◽  
Symmetry Principle ◽  
R Matrix ◽  
Exchange Algebra ◽  
Coset Spaces ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We derive, within the Hamiltonian formalism, the classical exchange algebra of a lambda deformed string sigma model in a symmetric space directly from a 4d holomorphic Chern-Simons theory. The explicit forms of the extended Lax connection and R-matrix entering the Maillet bracket of the lambda model are explained from a symmetry principle. This approach, based on a gauge theory, may provide a mechanism for taming the non-ultralocality that afflicts most of the integrable string theories propagating in coset spaces.

scholarly journals Asymptotic symmetries of Maxwell Chern–Simons gravity with torsion

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
H. Adami ◽  
P. Concha ◽  
E. Rodríguez ◽  
H. R. Safari
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Coupling Constants ◽  
Simons Theory ◽  
Asymptotic Symmetry ◽  
Chern Simons ◽  
Asymptotic Symmetries ◽  
Chern Simons Theory

AbstractWe present a three-dimensional Chern–Simons gravity based on a deformation of the Maxwell algebra. This symmetry allows introduction of a non-vanishing torsion to the Maxwell Chern–Simons theory, whose action recovers the Mielke–Baekler model for particular values of the coupling constants. By considering suitable boundary conditions, we show that the asymptotic symmetry is given by the $$\widehat{{\mathfrak {bms}}}_3\oplus {\mathfrak {vir}}$$ bms ^ 3 ⊕ vir algebra with three independent central charges.

scholarly journals Sigma models on flags

2019 ◽  
Vol 6 (2) ◽  
Author(s):  
Kantaro Ohmori ◽  
Nathan Seiberg ◽  
Shu-Heng Shao
Keyword(s):  
Sigma Models ◽  
Flag Manifold ◽  
Target Space ◽  
Global Symmetry ◽  
Specific Focus ◽  
Non Linear ◽  
Linear Sigma Models ◽  
Special Case

We study (1+1)-dimensional non-linear sigma models whose target space is the flag manifold U(N)\over U(N_1)\times U(N_2)\cdots U(N_m), with a specific focus on the special case U(N)/U(1)^{N}U(N)/U(1)N. These generalize the well-known \mathbb{CP}^{N-1}ℂℙN−1 model. The general flag model exhibits several new elements that are not present in the special case of the \mathbb{CP}^{N-1}ℂℙN−1 model. It depends on more parameters, its global symmetry can be larger, and its ’t Hooft anomalies can be more subtle. Our discussion based on symmetry and anomaly suggests that for certain choices of the integers N_INI and for specific values of the parameters the model is gapless in the IR and is described by an SU(N)_1SU(N)1 WZW model. Some of the techniques we present can also be applied to other cases.

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