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Chiral Algebras of (0, 2) Sigma Models: Beyond Perturbation Theory
, 2008
"... We explore the nonperturbative aspects of the chiral algebras of N = (0,2) sigma models, which perturbatively are intimately related to the theory of chiral differential operators (CDOs). The grading by charge and scaling dimension is anomalous if the first Chern class of the target space is nonzero ..."
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We explore the nonperturbative aspects of the chiral algebras of N = (0,2) sigma models, which perturbatively are intimately related to the theory of chiral differential operators (CDOs). The grading by charge and scaling dimension is anomalous if the first Chern class of the target space is nonzero. This has some nontrivial consequences for the chiral algebra. As an example, we study the case where the target space is CP 1, and show that worldsheet instantons trivialize the chiral algebra entirely. Consequently, supersymmetry is spontaneously broken in this model. We then turn to a closer look at the supersymmetry breaking from the viewpoint of Morse theory on loop space. We find that instantons interpolate between pairs of perturbative supersymmetric states with different fermionic numbers, hence lifting them out of the supersymmetric spectrum. Our results reveal that a “quantum ” deformation of the geometry of the target space leads to a trivialization of the kernels of certain twisted Dirac operators on CP 1.
3. Finite Type Substacks of [A/(C×) V] 23
, 904
"... Abstract. We introduce a geometric completion of the stack of maps from stable marked curves to the quotient stack pt/C × , and use it to construct some gaugetheoretic analogues of the GromovWitten invariants. We also indicate the generalization of these invariants to the quotient stacks [X/C ×], ..."
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Abstract. We introduce a geometric completion of the stack of maps from stable marked curves to the quotient stack pt/C × , and use it to construct some gaugetheoretic analogues of the GromovWitten invariants. We also indicate the generalization of these invariants to the quotient stacks [X/C ×], where X is a smooth proper complex algebraic variety.
Basic Books in the Fall of 2013.
"... The lights were dimmed... After a few long seconds of silence the movie theater went dark. Then the giant screen lit up, and black letters appeared on the white background: Red Fave Productions ..."
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The lights were dimmed... After a few long seconds of silence the movie theater went dark. Then the giant screen lit up, and black letters appeared on the white background: Red Fave Productions
REVIEW ARTICLE What the characters of irreducible subrepresentations of Jordan cells can tell us about LCFT
"... Abstract. In this article, we review some aspects of logarithmic conformal field theories which can be inferred from the characters of irreducible submodules of indecomposable modules. We will mainly consider the W(2, 2p − 1, 2p − 1, 2p − 1) series of triplet algebras and a bit logarithmic extension ..."
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Abstract. In this article, we review some aspects of logarithmic conformal field theories which can be inferred from the characters of irreducible submodules of indecomposable modules. We will mainly consider the W(2, 2p − 1, 2p − 1, 2p − 1) series of triplet algebras and a bit logarithmic extensions of the minimal Virasoro models. Since in all known examples of logarithmic conformal field theories the vacuum representation of the maximally extended chiral symmetry algebra is an irreducible submodule of a larger, indecomposable module, its character provides a lot of nontrivial information about the theory such as a set of functions which spans the space of all torus amplitudes. Despite such characters being modular forms of inhomogeneous weight, they fit in the ADETclassification of fermionic sum representations. Thus, they show that logarithmic conformal field theories naturally have to be taken into account when attempting to classify rational conformal field theories.
OF THE UNIVERSITY OF MINNESOTA BY
, 2012
"... Perturbative and nonperturbative aspects of heterotic sigma models ..."
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What the characters of irreducible subrepresentations of Jordan cells can tell us about LCFT
"... In this article, we review some aspects of logarithmic conformal field theories which can be inferred from the characters of irreducible submodules of indecomposable modules. We will mainly consider the W(2, 2p − 1, 2p − 1, 2p − 1) series of triplet algebras and a bit logarithmic extensions of the ..."
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In this article, we review some aspects of logarithmic conformal field theories which can be inferred from the characters of irreducible submodules of indecomposable modules. We will mainly consider the W(2, 2p − 1, 2p − 1, 2p − 1) series of triplet algebras and a bit logarithmic extensions of the minimal Virasoro models. Since in all known examples of logarithmic conformal field theories the vacuum representation of the maximally extended chiral symmetry algebra is an irreducible submodule of a larger, indecomposable module, its character provides a lot of nontrivial information about the theory such as a set of functions which spans the space of all torus amplitudes. Despite such characters being modular forms of inhomogeneous weight, they fit in the ADETclassification of fermionic sum representations. Thus, they show that logarithmic conformal field theories naturally have to be taken into account when attempting to classify rational conformal field theories.