Topic
Structure constants
About: Structure constants is a research topic. Over the lifetime, 828 publications have been published within this topic receiving 19864 citations.
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Papers
TL;DR: In this article, the deformation theory for algebras is studied in terms of the set of structure constants as a parameter space, and an example justifying the choice of parameter space is given.
Abstract: CHAPTER I. The deformation theory for algebras 1. Infinitesimal deformations of an algebra 2. Obstructions 3. Trivial deformations 4. Obstructions to derivations and the squaring operation 5. Obstructions are cocycles 6. Additivity and integrability of the square 7. Restricted deformation theories and their cohomology theories 8. Rigidity of fields in the commutative theory CHAPTER II. The parameter space 1. The set of structure constants as parameter space for the deformation theory 2. Central algebras and an example justifying the choice of parameter space 3. The automorphism group as a parameter space, and examples of obstructions to derivations 4. A fiber space over the parameter space, and the upper semicontinuity theorem 5. An example of a restricted theory and the corresponding modular group CHAPTER III. The deformation theory for graded and filtered rings 1. Graded, filtered, and developable rings 2. The Hochschild theory for developable rings 3. Developable rings as deformations of their associated graded rings 4. Trivial deformations and a criterion for rigidity 5. Restriction to the commutative theory 6. Deformations of power series rings
1,731 citations
TL;DR: In this paper, an analytic expression for the three-point function of the exponential fields in the Liouville field theory on a sphere is proposed and verified numerically that it satisfies conformal bootstrap equations, i.e., that the operator algebra thus defined is associative.
Abstract: An analytic expression is proposed for the three-point function of the exponential fields in the Liouville field theory on a sphere. In the classical limit it coincides with what the classical Liouville theory predicts. Using this function as the structure constant of the operator algebra we construct the four-point function of the exponential fields and verify numerically that it satisfies the conformal bootstrap equations, i.e., that the operator algebra thus defined is associative. We consider also the Liouville reflection amplitude which follows explicitly from the structure constants.
964 citations
TL;DR: In this article, rational conformal field theory is formulated in terms of a symmetric special Frobenius algebra A and its representations, which is an algebra in the modular tensor category of Moore-Seiberg data of the underlying chiral CFT.
538 citations
TL;DR: In this paper, rational conformal field theory is formulated in terms of a symmetric special Frobenius algebra A and its representations, which is an algebra in the modular tensor category of Moore-Seiberg data of the underlying chiral CFT.
Abstract: We formulate rational conformal field theory in terms of a symmetric special Frobenius algebra A and its representations. A is an algebra in the modular tensor category of Moore-Seiberg data of the underlying chiral CFT. The multiplication on A corresponds to the OPE of boundary fields for a single boundary condition. General boundary conditions are A-modules, and (generalised) defect lines are A-A-bimodules.
The relation with three-dimensional TFT is used to express CFT data, like structure constants or torus and annulus coefficients, as invariants of links in three-manifolds. We compute explicitly the ordinary and twisted partition functions on the torus and the annulus partition functions. We prove that they satisfy consistency conditions, like modular invariance and NIM-rep properties.
We suggest that our results can be interpreted in terms of non-commutative geometry over the modular tensor category of Moore-Seiberg data.
389 citations
TL;DR: In this paper, the authors studied the N = 2 superconformal index in various interesting limits, such that only states annihilated by more than one supercharge contribute, and showed that the index can always be interpreted as a correlator in a two-dimensional topological theory.
Abstract: We study the N=2 four-dimensional superconformal index in various interesting limits, such that only states annihilated by more than one supercharge contribute. Extrapolating from the SU(2) generalized quivers, which have a Lagrangian description, we conjecture explicit formulae for all A-type quivers of class S, which in general do not have one. We test our proposals against several expected dualities. The index can always be interpreted as a correlator in a two-dimensional topological theory, which we identify in each limit as a certain deformation of two-dimensional Yang-Mills theory. The structure constants of the topological algebra are diagonal in the basis of Macdonald polynomials of the holonomies.
381 citations
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| Year | Papers |
|---|---|
| 2025 | 1 |
| 2024 | 1 |
| 2023 | 16 |
| 2022 | 28 |
| 2021 | 48 |
| 2020 | 38 |