scholarly journals Towards formalization of the soliton counting technique for the Khovanov–Rozansky invariants in the deformed ℛ-matrix approach

2018 ◽  
Vol 33 (36) ◽  
pp. 1850221
Author(s):  
A. Anokhina
Keyword(s):  
Field Theory ◽  
Intermediate Stage ◽  
Diagram Technique ◽  
Mathematical Treatment ◽  
Matrix Approach ◽  
Detailed Review ◽  
Counting Technique ◽  
Cohomological Field Theory

We consider recently developed Cohomological Field Theory (CohFT) soliton counting diagram technique for Khovanov (Kh) and Khovanov–Rozansky (KhR) invariants.[Formula: see text] Although, the expectation to obtain a new way for computing the invariants has not yet come true, we demonstrate that soliton counting technique can be totally formalized at an intermediate stage, at least in particular cases. We present the corresponding algorithm, based on the approach involving deformed [Formula: see text]-matrix and minimal positive division, developed previously in Ref. 3. We start from a detailed review of the minimal positive division approach, comparing it with other methods, including the rigorous mathematical treatment.4 Pieces of data obtained within our approach are presented in the Appendices.

Diagram technique of 1/N expansion in a matrix model of field theory

1986 ◽  
Vol 66 (3) ◽  
pp. 243-252 ◽  
Author(s):  
N. V. Goncharov ◽  
A. A. Slavnov
Keyword(s):  
Field Theory ◽  
Matrix Model ◽  
Diagram Technique

scholarly journals Noncommutative cohomological field theory and GMS soliton

2002 ◽  
Vol 43 (2) ◽  
pp. 872-896 ◽  
Author(s):  
Akifumi Sako ◽  
Shin-Ichiro Kuroki ◽  
Tomomi Ishikawa
Keyword(s):  
Field Theory ◽  
Cohomological Field Theory

THE AFFINE TODA S-MATRICES vs PERTURBATION THEORY

1993 ◽  
Vol 08 (01) ◽  
pp. 115-134 ◽  
Author(s):  
RYU SASAKI ◽  
FREDDY PERMANA ZEN
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Fourth Order ◽  
Calculation Method ◽  
Coupling Constants ◽  
Matrix Approach ◽  
Bootstrap Equation ◽  
S Matrix ◽  
Complete Form ◽  
Toda Field Theory

We present perturbative calculations for the Affine Toda Field Theory (ATFT) S-matrices to the second order in the coupling constants for [Formula: see text] and [Formula: see text] in general, to the fourth order for [Formula: see text] theory as well as to the sixth order for [Formula: see text] theory. Conventional Feynman–Dyson calculation method and the dispersion approach are used to calculate the complete form of the perturbation amplitudes in contrast to the pole residues in previous papers. The results agree with those S-matrices obtained in the S-matrix approach, namely those based on analyticity, unitarity, crossing and bootstrap equation.

scholarly journals Matrix factorizations and cohomological field theories

2016 ◽  
Vol 2016 (714) ◽  
pp. 1-122 ◽  
Author(s):  
Alexander Polishchuk ◽  
Arkady Vaintrob
Keyword(s):  
Field Theory ◽  
Field Theories ◽  
Matrix Factorizations ◽  
Hypersurface Singularity ◽  
Algebraic Construction ◽  
Cohomological Field Theories ◽  
Cohomological Field Theory

AbstractWe give a purely algebraic construction of a cohomological field theory associated with a quasihomogeneous isolated hypersurface singularity

scholarly journals DUBROVIN’S SUPERPOTENTIAL AS A GLOBAL SPECTRAL CURVE

2017 ◽  
Vol 18 (3) ◽  
pp. 449-497 ◽  
Author(s):  
P. Dunin-Barkowski ◽  
P. Norbury ◽  
N. Orantin ◽  
A. Popolitov ◽  
S. Shadrin
Keyword(s):  
Field Theory ◽  
Spectral Curve ◽  
Frobenius Manifold ◽  
Simple Point ◽  
Topological Recursion ◽  
Cohomological Field Theory

We apply the spectral curve topological recursion to Dubrovin’s universal Landau–Ginzburg superpotential associated to a semi-simple point of any conformal Frobenius manifold. We show that under some conditions the expansion of the correlation differentials reproduces the cohomological field theory associated with the same point of the initial Frobenius manifold.

scholarly journals Invariants of four-manifolds with flows via cohomological field theory

2014 ◽  
Author(s):  
Hugo Garcia-Compeân ◽  
Roberto Santos-Silva ◽  
Alberto Verjovsky
Keyword(s):  
Field Theory ◽  
Probability Measure ◽  
Vector Fields ◽  
Invariant Probability Measure ◽  
Yang Mills ◽  
Higher Dimensional ◽  
Coupling Dynamics ◽  
Four Manifolds ◽  
Cohomological Field Theory ◽  
Asymptotic Cycles

This chapter argues that the Jones–Witten invariants can be generalized for smooth, nonsingular vector fields with invariant probability measure on three-manifolds, thus giving rise to new invariants of dynamical systems. After a short survey of cohomological field theory for Yang–Mills fields, Donaldson–Witten invariants are generalized to four-dimensional manifolds with non-singular smooth flows generated by homologically non-trivial p-vector fields. The chapter studies the case of Kähler manifolds by using the Witten's consideration of the strong coupling dynamics of N = 1 supersymmetric Yang–Mills theories. The whole construction is performed by implementing the notion of higher-dimensional asymptotic cycles. In the process Seiberg–Witten invariants are also described within this context. Finally, the chapter gives an interpretation of the asymptotic observables of four-manifolds in the context of string theory with flows.

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