Results 81 to 90 of about 33,027 (196)
Holomorphic field theories and higher algebra
Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 2903-2974, October 2025.Abstract Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogs of the rich interplay between Riemann surfaces, Virasoro and Kac‐Moody Lie algebras, and conformal blocks. We introduce a panoply of examples from physics — field theories that are holomorphic in nature, such as holomorphic Chern‐Simons ...
Owen Gwilliam, Brian R. Williams
wiley +1 more source
Difference equations: From Berry connections to the Coulomb branch
SciPost PhysicsIn recent work, we demonstrated that a spectral variety for the Berry connection of a 2d $\mathcal{N}=(2,2)$ GLSM with Kähler vacuum moduli space $X$ and Abelian flavour symmetry is the support of a sheaf induced by a certain action on the equivariant ...
Andrea E. V. Ferrari, Daniel Zhang
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The Global Symmetry Group of Quantum Spectral Beams and Geometric Phase Factors
Advances in Mathematical Physics, 2015 We propose a cohomological modelling schema of quantum state spaces and their connectivity structures in relation to the formulation of global geometric phase phenomena. In the course of this schema, we introduce the notion of Hermitian differential line
Elias Zafiris
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Quantum cohomology and free-field representation
Nuclear Physics B, 1998 In our previous article we have proposed that the Virasoro algebra controls the quantum cohomology of Fano varieties at all genera. In this paper we construct a free field description of Virasoro operators and quantum cohomology. We shall show that to each even (odd) homology class of a K hler manifold we have a free bosonic (fermionic) field and ...
Eguchi, Tohru +2 more
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A rigorous definition of fiberwise quantum cohomology and equivariant quantum cohomology [PDF]
Communications in Analysis and Geometry, 1998 Since the proposal of the notion of quantum cohomology by the physicist \textit{C. Vafa} [in: `Essays on mirror manifolds', 96-119 (1992; Zbl 0827.58073)] and its mathematical foundation by \textit{Y. Ruan} and \textit{G. Tian} [J. Differ. Geom. 42, 259-367 (1995; Zbl 0860.58005)] for semi-positive symplectic manifolds, the quantum cohomology has ...
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Symmetry, Integrability and Geometry: Methods and Applications, 2009 In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are ''associativity'' or ''factorization'' conditions on the operator product expansion (OPE) of the theory,
Stefan Hollands
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(2, 2) geometry from gauge theory
Journal of High Energy Physics, 2018 Using gauge theory, we describe how to construct generalized Kähler geometries with (2, 2) two-dimensional supersymmetry, which are analogues of familiar examples like projective spaces and Calabi-Yau manifolds. For special cases, T-dual descriptions can
João Caldeira +2 more
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Cohomology of Infinitesimal Quantum Algebras
Journal of Algebra, 2000 In this very technically written paper the author shows an isomorphism between two functors defined by the quantum Frobenius homomorphism, which enables the definition of the Frobenius homomorphism in the cohomology of infinitesimal quantum algebras.
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, 1996 We discuss a general quantum theoretical example of quantum cohomology and show that various mathematical aspects of quantum cohomology have quantum mechanical and also observable significance.
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Quantum cohomology of flag manifolds
Advances in Mathematics, 2003 The (small) quantum cohomology ring of a flag manifold F encodes enumerative geometry of rational curves on F. We give a proof of the presentation of the ring and of a quantum Giambelli formula, which is more direct and geometric than the previously known proof.
openaire +3 more sources