scholarly journals Degenerations of Calabi–Yau threefolds and BCOV invariants

2015 ◽  
Vol 26 (04) ◽  
pp. 1540010 ◽  
Author(s):  
Ken-Ichi Yoshikawa
Keyword(s):  
Field Theories ◽  
Nucl Phys ◽  
Analytic Torsion ◽  
Logarithmic Divergence ◽  
Topological Field ◽  
String Amplitudes ◽  
The Given ◽  
Stable Reduction ◽  
Math Phys ◽  
Torsion Invariant

In [M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Holomorphic anomalies in topological field theories, Nucl. Phys. B405 (1993) 279–304; M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Kodaira–Spencer theory of gravity and exact results for quantum string amplitudes, Commun. Math. Phys.165 (1994) 311–427], by expressing the physical quantity F1 in two distinct ways, Bershadsky–Cecotti–Ooguri–Vafa discovered a remarkable equivalence between Ray–Singer analytic torsion and elliptic instanton numbers for Calabi–Yau threefolds. After their discovery, in [H. Fang, Z. Lu and K.-I. Yoshikawa, Analytic torsion for Calabi–Yau threefolds, J. Differential Geom.80 (2008) 175–250], a holomorphic torsion invariant for Calabi–Yau threefolds corresponding to F1, called BCOV invariant, was constructed. In this article, we study the asymptotic behavior of BCOV invariants for algebraic one-parameter degenerations of Calabi–Yau threefolds. We prove the rationality of the coefficient of logarithmic divergence and give its geometric expression by using a semi-stable reduction of the given family.

scholarly journals BRST QUANTIZATION AND THE PRODUCT FORMULA FOR THE RAY-SINGER TORSION

1995 ◽  
Vol 10 (12) ◽  
pp. 1779-1805 ◽  
Author(s):  
CHARLES NASH ◽  
DENJOE O’CONNOR
Keyword(s):  
Finite Elements ◽  
Topological Field Theories ◽  
Brst Quantization ◽  
Product Formula ◽  
Field Theories ◽  
Analytic Torsion ◽  
Quantum Field ◽  
Infinite Dimensional ◽  
New Class ◽  
Topological Field

We give a quantum field theoretic derivation of the formula obeyed by the Ray-Singer torsion on product manifolds. Such a derivation has proved elusive up to now. We use a BRST formalism which introduces the idea of an infinite dimensional Universal Gauge Fermion, and is of independent interest, being applicable to situations other than the ones considered here. We are led to a new class of Fermionic topological field theories. Our methods are also applicable to combinatorially defined manifolds and methods of discrete approximation, such as the use of a simplicial lattice or finite elements. The topological field theories discussed provide a natural link between the combinatorial and analytic torsion.

Beyond the Standard Model

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.

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.

scholarly journals Topological field theories on manifolds with Wu structures

2017 ◽  
Vol 29 (05) ◽  
pp. 1750015 ◽  
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.

scholarly journals DNA Mutations via Chern–Simons Currents

2021 ◽  
Vol 136 (10) ◽  
Author(s):  
Francesco Bajardi ◽  
Lucia Altucci ◽  
Rosaria Benedetti ◽  
Salvatore Capozziello ◽  
Maria Rosaria Del Sorbo ◽  
...  
Keyword(s):  
Human Gene ◽  
Simons Theory ◽  
Topological Field Theory ◽  
Structure And Dynamics ◽  
Dna Mutations ◽  
Analogue Gravity ◽  
Topological Field ◽  
The Given ◽  
Chern Simons ◽  
Chern Simons Theory

AbstractWe test the validity of a possible schematization of DNA structure and dynamics based on the Chern–Simons theory, that is a topological field theory mostly considered in the context of effective gravity theories. By means of the expectation value of the Wilson Loop, derived from this analogue gravity approach, we find the point-like curvature of genomic strings in KRAS human gene and COVID-19 sequences, correlating this curvature with the genetic mutations. The point-like curvature profile, obtained by means of the Chern–Simons currents, can be used to infer the position of the given mutations within the genetic string. Generally, mutations take place in the highest Chern–Simons current gradient locations and subsequent mutated sequences appear to have a smoother curvature than the initial ones, in agreement with a free energy minimization argument.

The Vilkovisky-De Witt effective action in BF-type topological field theories

1991 ◽  
Vol 269 (1-2) ◽  
pp. 116-122 ◽  
Author(s):  
Danny Birmingham ◽  
H.T. Cho ◽  
R. Kantowski ◽  
M. Rakowski
Keyword(s):  
Topological Field Theories ◽  
Effective Action ◽  
Field Theories ◽  
Topological Field
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