The algebraic structure of cohomological field theory

Abstract L∞ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze the algebraic structure of Gauged Double Field Theory in the generalized flux formalism. The symmetry transformations consist of a generalized deformed Lie derivative and double Lorentz transformations. We obtain all the non-trivial products in a closed form considering a generalized Kerr-Schild ansatz for the generalized frame and we include a linear perturbation for the generalized dilaton. The off-shell structure can be cast in an L3 algebra and when one considers dynamics the former is exactly promoted to an L4 algebra. The present computations show the fully algebraic structure of the fundamental charged heterotic string and the $$ {L}_3^{\mathrm{gauge}} $$ L 3 gauge structure of (Bosonic) Enhanced Double Field Theory.

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Cohomological field theory from field-space cohomology

Nuclear Physics B ◽

10.1016/0550-3213(91)90469-e ◽

1991 ◽

Vol 357 (1) ◽

pp. 271-288 ◽

Cited By ~ 2

Author(s):

Steven B. Giddings

Keyword(s):

Field Theory ◽

Cohomological Field Theory ◽

Space Cohomology

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Renormalization and Hopf algebraic structure of the five-dimensional quartic tensor field theory

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8113/48/48/485204 ◽

2015 ◽

Vol 48 (48) ◽

pp. 485204 ◽

Cited By ~ 1

Author(s):

Remi C Avohou ◽

Vincent Rivasseau ◽

Adrian Tanasa

Keyword(s):

Field Theory ◽

Algebraic Structure ◽

Tensor Field

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Noncommutative cohomological field theory and GMS soliton

Journal of Mathematical Physics ◽

10.1063/1.1418428 ◽

2002 ◽

Vol 43 (2) ◽

pp. 872-896 ◽

Cited By ~ 4

Author(s):

Akifumi Sako ◽

Shin-Ichiro Kuroki ◽

Tomomi Ishikawa

Keyword(s):

Field Theory ◽

Cohomological Field Theory

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

International Journal of Modern Physics A ◽

10.1142/s0217751x18502214 ◽

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.

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