11,224 research outputs found
Quantum hypermultiplet moduli spaces in N=2 string vacua: a review
The hypermultiplet moduli space M_H in type II string theories compactified
on a Calabi-Yau threefold X is largely constrained by supersymmetry (which
demands quaternion-K\"ahlerity), S-duality (which requires an isometric action
of SL(2, Z)) and regularity. Mathematically, M_H ought to encode all
generalized Donaldson-Thomas invariants on X consistently with wall-crossing,
modularity and homological mirror symmetry. We review recent progress towards
computing the exact metric on M_H, or rather the exact complex contact
structure on its twistor space.Comment: 31 pages; Contribution to the Proceedings of String Math 2012; v2:
references added, misprints corrected, published versio
D3-instantons, Mock Theta Series and Twistors
The D-instanton corrected hypermultiplet moduli space of type II string
theory compactified on a Calabi-Yau threefold is known in the type IIA picture
to be determined in terms of the generalized Donaldson-Thomas invariants,
through a twistorial construction. At the same time, in the mirror type IIB
picture, and in the limit where only D3-D1-D(-1)-instanton corrections are
retained, it should carry an isometric action of the S-duality group SL(2,Z).
We prove that this is the case in the one-instanton approximation, by
constructing a holomorphic action of SL(2,Z) on the linearized twistor space.
Using the modular invariance of the D4-D2-D0 black hole partition function, we
show that the standard Darboux coordinates in twistor space have modular
anomalies controlled by period integrals of a Siegel-Narain theta series, which
can be canceled by a contact transformation generated by a holomorphic mock
theta series.Comment: 42 pages; discussion of isometries is amended; misprints correcte
An Introduction To The Web-Based Formalism
This paper summarizes our rather lengthy paper, "Algebra of the Infrared:
String Field Theoretic Structures in Massive Field Theory In
Two Dimensions," and is meant to be an informal, yet detailed, introduction and
summary of that larger work.Comment: 50 pages, 40 figure
Invariable generation and the chebotarev invariant of a finite group
A subset S of a finite group G invariably generates G if G = <hsg(s) j s 2 Si
> for each choice of g(s) 2 G; s 2 S. We give a tight upper bound on the
minimal size of an invariable generating set for an arbitrary finite group G.
In response to a question in [KZ] we also bound the size of a randomly chosen
set of elements of G that is likely to generate G invariably. Along the way we
prove that every finite simple group is invariably generated by two elements.Comment: Improved versio
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