TOPOLOGICAL GRAVITY LOCALIZATION ON A δ-FUNCTION LIKE BRANE

In the celebrated Plebanski formalism of topological gravity, the constraints connecting topological field theories and gravity are imposed in spacetimes with trivial topology. In the braneworld context there are two distinct regions of the spacetime, namely, the bulk and the braneworld volume. In this work we show how to construct topological classical gravity in a scenario containing one extra dimension and a δ-function like three-brane which naturally emerges from a spontaneously broken discrete symmetry. Starting from a D = 5 theory we obtain the action for General Relativity in the Palatini form in the bulk as well as in the braneworld volume. This result is important for future insights about quantum gravity on brane scenarios.

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Topological field theories on manifolds with Wu structures

Reviews in Mathematical Physics ◽

10.1142/s0129055x17500155 ◽

2017 ◽

Vol 29 (05) ◽

pp. 1750015 ◽

Cited By ~ 6

Author(s):

Samuel Monnier

Keyword(s):

Topological Field Theories ◽

Geometric Quantization ◽

Discrete Symmetry ◽

Local System ◽

Field Theories ◽

Simons Theory ◽

General Point ◽

Topological Field ◽

Generalized Cohomology ◽

Chern Simons

We construct invertible field theories generalizing abelian prequantum spin Chern–Simons theory to manifolds of dimension [Formula: see text] endowed with a Wu structure of degree [Formula: see text]. After analyzing the anomalies of a certain discrete symmetry, we gauge it, producing topological field theories whose path integral reduces to a finite sum, akin to Dijkgraaf–Witten theories. We take a general point of view where the Chern–Simons gauge group and its couplings are encoded in a local system of integral lattices. The Lagrangian of these theories has to be interpreted as a class in a generalized cohomology theory in order to obtain a gauge invariant action. We develop a computationally friendly cochain model for this generalized cohomology and use it in a detailed study of the properties of the Wu Chern–Simons action. In the 3-dimensional spin case, the latter provides a definition of the “fermionic correction” introduced recently in the literature on fermionic symmetry protected topological phases. In order to construct the state space of the gauged theories, we develop an analogue of geometric quantization for finite abelian groups endowed with a skew-symmetric pairing. The physical motivation for this work comes from the fact that in the [Formula: see text] case, the gauged 7-dimensional topological field theories constructed here are essentially the anomaly field theories of the 6-dimensional conformal field theories with [Formula: see text] supersymmetry, as will be discussed elsewhere.

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MATRIX MODELS WITHOUT SCALING LIMIT

International Journal of Modern Physics A ◽

10.1142/s0217751x93001211 ◽

1993 ◽

Vol 08 (17) ◽

pp. 2973-2992 ◽

Cited By ~ 28

Author(s):

L. BONORA ◽

C. S. XIONG

Keyword(s):

Matrix Models ◽

Topological Field Theories ◽

Continuum Limit ◽

Scaling Limit ◽

Exact Result ◽

Field Theories ◽

Kdv Hierarchy ◽

The Matrix ◽

Topological Field ◽

Topological Gravity

In the context of Hermitian one-matrix models we show that the emergence of the NLS hierarchy and of its reduction, the KdV hierarchy, is an exact result of the lattice characterizing the matrix model. Said otherwise, we are not obliged to take a continuum limit to find these hierarchies. We interpret this result as an indication of the topological nature of them. We discuss the topological field theories associated with both and discuss the connection with topological field theories coupled to topological gravity already studied in the literature.

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GAUGE FIXING TOPOLOGICAL YANG-MILLS

International Journal of Modern Physics A ◽

10.1142/s0217751x90000635 ◽

1990 ◽

Vol 05 (07) ◽

pp. 1369-1381 ◽

Cited By ~ 15

Author(s):

ROBERT MYERS

Keyword(s):

Gauge Symmetry ◽

Topological Field Theories ◽

Correlation Functions ◽

Field Theories ◽

Yang Mills ◽

Gauge Fixing ◽

Topological Field ◽

Topological Gravity

We examine two methods of fixing the gauge symmetry in Witten’s topological Yang-Mills theory. We find that both procedures produce the same nontrivial correlation functions. Our results also apply to other topological field theories, such as topological gravity.

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Beyond the Standard Model

10.1093/oso/9780198788393.003.0026 ◽

2017 ◽

Author(s):

Laurent Baulieu ◽

John Iliopoulos ◽

Roland Sénéor

Keyword(s):

Field Theory ◽

General Relativity ◽

Supergravity Models ◽

Standard Model ◽

Field Theories ◽

Beyond The Standard Model ◽

Super Symmetry ◽

The Standard Model ◽

Topological Field ◽

Supersymmetric Theories

The motivation for supersymmetry. The algebra, the superspace, and the representations. Field theory models and the non-renormalisation theorems. Spontaneous and explicit breaking of super-symmetry. The generalisation of the Montonen–Olive duality conjecture in supersymmetric theories. The remarkable properties of extended supersymmetric theories. A brief discussion of twisted supersymmetry in connection with topological field theories. Attempts to build a supersymmetric extention of the standard model and its experimental consequences. The property of gauge supersymmetry to include general relativity and the supergravity models.

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A COMMENT ON TOPOLOGICAL FIELD THEORY QUANTIZATION AND STOCHASTIC PROCESSES

International Journal of Modern Physics A ◽

10.1142/s0217751x90001604 ◽

1990 ◽

Vol 05 (19) ◽

pp. 3777-3786 ◽

Cited By ~ 2

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.

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