Chiral strings, topological branes, and a generalised Weyl-invariance

2019 ◽  
Vol 34 (06n07) ◽  
pp. 1950031 ◽  
Author(s):  
Alex S. Arvanitakis
Keyword(s):  
Field Theory ◽  
Sigma Model ◽  
Space Time ◽  
Symplectic Space ◽  
Topological Field Theory ◽  
Brst Operator ◽  
Weyl Invariance ◽  
Fixed Action ◽  
Twistor Strings ◽  
Topological Field

We introduce a sigma model Lagrangian generalising a number of new and old models which can be thought of as chiral, including the Schild string, ambitwistor strings, and the recently introduced tensionless AdS twistor strings. This “chiral sigma model” describes maps from a [Formula: see text]-brane worldvolume into a symplectic space and is manifestly invariant under diffeomorphisms as well as under a “generalised Weyl invariance” acting on space–time coordinates and worldvolume fields simultaneously. Construction of the Batalin–Vilkovisky master action leads to a BRST operator under which the gauge-fixed action is BRST-exact; we discuss whether this implies that the chiral brane sigma model defines a topological field theory.

scholarly journals Topological field theories induced by twisted R-Poisson structure in any dimension

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Athanasios Chatzistavrakidis
Keyword(s):  
Field Theory ◽  
Poisson Structure ◽  
Sigma Model ◽  
Three Dimensions ◽  
Target Space ◽  
Field Theories ◽  
Topological Field Theory ◽  
Covariant Formulation ◽  
Topological Field ◽  
Poisson Sigma Model

Abstract We construct a class of topological field theories with Wess-Zumino term in spacetime dimensions ≥ 2 whose target space has a geometrical structure that suitably generalizes Poisson or twisted Poisson manifolds. Assuming a field content comprising a set of scalar fields accompanied by gauge fields of degree (1, p − 1, p) we determine a generic Wess-Zumino topological field theory in p + 1 dimensions with background data consisting of a Poisson 2-vector, a (p + 1)-vector R and a (p + 2)-form H satisfying a specific geometrical condition that defines a H-twisted R-Poisson structure of order p + 1. For this class of theories we demonstrate how a target space covariant formulation can be found by means of an auxiliary connection without torsion. Furthermore, we study admissible deformations of the generic class in special spacetime dimensions and find that they exist in dimensions 2, 3 and 4. The two-dimensional deformed field theory includes the twisted Poisson sigma model, whereas in three dimensions we find a more general structure that we call bi-twisted R-Poisson. This extends the twisted R-Poisson structure of order 3 by a non-closed 3-form and gives rise to a topological field theory whose covariant formulation requires a connection with torsion and includes a twisted Poisson sigma model in three dimensions as a special case. The relation of the corresponding structures to differential graded Q-manifolds based on the degree shifted cotangent bundle T*[p]T*[1]M is discussed, as well as the obstruction to them being QP-manifolds due to the Wess-Zumino term.

A COMMENT ON TOPOLOGICAL FIELD THEORY QUANTIZATION AND STOCHASTIC PROCESSES

1990 ◽  
Vol 05 (19) ◽  
pp. 3777-3786 ◽  
Author(s):  
L.F. CUGLIANDOLO ◽  
G. LOZANO ◽  
H. MONTANI ◽  
F.A. SCHAPOSNIK
Keyword(s):  
Field Theory ◽  
Equilibrium State ◽  
Stochastic Processes ◽  
Topological Field Theories ◽  
Topological Charge ◽  
Field Theories ◽  
Langevin Equations ◽  
Topological Field Theory ◽  
Topological Field

We discuss the relation between different quantization approaches to topological field theories by deriving a connection between Bogomol’nyi and Langevin equations for stochastic processes which evolve towards an equilibrium state governed by the topological charge.

TETRAHEDRA AND POLYNOMIAL EQUATIONS IN TOPOLOGICAL FIELD THEORY

1991 ◽  
Vol 06 (20) ◽  
pp. 3571-3598 ◽  
Author(s):  
NOUREDDINE CHAIR ◽  
CHUAN-JIE ZHU
Keyword(s):  
Field Theory ◽  
Topological Field Theory ◽  
Fundamental Representation ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Witten Theory ◽  
Topological Field ◽  
General Program ◽  
The One ◽  
Chern Simons

Some tetrahedra in SUk(2) Chern-Simons-Witten theory are computed. The results can be used to compute an arbitrary tetrahedron inductively by fusing with the fundamental representation. The results obtained are in agreement with those of quantum groups. By associating a (finite) topological field theory (FTFT) to every rational conformal field theory (RCFT), we show that the pentagon and hexagon equations in RCFT follow directly from some skein relations in FTFT. By generalizing the operation of surgery on links in FTFT, we also derive an explicit expression for the modular transformation matrix S(k) of the one-point conformal blocks on a torus in RCFT and the equations satisfied by S(k), in agreement with those required in RCFT. The implication of our results on the general program of classifying RCFT is also discussed.

scholarly journals Chern–Simons–Rozansky–Witten topological field theory

2009 ◽  
Vol 823 (3) ◽  
pp. 403-427 ◽  
Author(s):  
Anton Kapustin ◽  
Natalia Saulina
Keyword(s):  
Field Theory ◽  
Topological Field Theory ◽  
Topological Field ◽  
Chern Simons

scholarly journals Topological Field Theory and Computing with Instantons

2017 ◽  
Vol 529 (12) ◽  
pp. 1700123 ◽  
Author(s):  
Massimiliano Di Ventra ◽  
Fabio L. Traversa ◽  
Igor V. Ovchinnikov
Keyword(s):  
Field Theory ◽  
Topological Field Theory ◽  
Topological Field

scholarly journals TOPOLOGICAL FIELD THEORY OF VORTICES OVER CLOSED KÄHLER MANIFOLD

1995 ◽  
Vol 10 (30) ◽  
pp. 4371-4385
Author(s):  
HYUK-JAE LEE
Keyword(s):  
Field Theory ◽  
Vortex Pair ◽  
Kähler Manifolds ◽  
Topological Field Theory ◽  
Kahler Manifolds ◽  
Topological Theory ◽  
Vortex Equations ◽  
Pair Model ◽  
Topological Field ◽  
Component Direction

We show that the vortex equations of the n-dimensional closed Kähler manifolds can be derived from Einstein-Hermitian equations of the (n+1)-dimensional closed Kähler manifolds by setting invariance under translation in the (n+1)th component direction. We construct the topological theory about the vortex pair model through the dimensional reduction of the topological BRST structure.

scholarly journals BRST-FIXED POINTS AND TOPOLOGICAL CONFORMAL SYMMETRY

1992 ◽  
Vol 07 (24) ◽  
pp. 2215-2222 ◽  
Author(s):  
TOSHIO NAKATSU ◽  
YUJI SUGAWARA
Keyword(s):  
Field Theory ◽  
Fixed Points ◽  
Conformal Symmetry ◽  
Topological Field Theory ◽  
Two Dimensional ◽  
Brst Transformation ◽  
Dimensional Gravity ◽  
Matter System ◽  
Topological Field ◽  
Topological Matter

We study the twisted version of the supersymmetric G/T = SU (n)/ U (1)⊗(n−1) gauged Wess-Zumino-Witten model. By studying its fixed points under BRST transformation this model is shown to be reduced to a simple topological Field theory, that is, the topological matter system in the K. Li's theory of two-dimensional gravity for the case of n = 2, and its generalization for n ≥ 3.

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