36 research outputs found
Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds
We present a proof of the mirror conjecture of Aganagic-Vafa
[arXiv:hep-th/0012041] and Aganagic-Klemm-Vafa [arXiv:hep-th/0105045] on disk
enumeration in toric Calabi-Yau 3-folds for all smooth semi-projective toric
Calabi-Yau 3-folds. We consider both inner and outer branes, at arbitrary
framing. In particular, we recover previous results on the conjecture for (i)
an inner brane at zero framing in the total space of the canonical line bundle
of the projective plane (Graber-Zaslow [arXiv:hep-th/0109075]), (ii) an outer
brane at arbitrary framing in the resolved conifold (Zhou [arXiv:1001.0447]),
and (iii) an outer brane at zero framing in the total space of the canonical
line bundle of the projective plane (Brini [arXiv:1102.0281, Section 5.3]).Comment: 39 pages, 11 figure
Quantum Group as Semi-infinite Cohomology
We obtain the quantum group as semi-infinite cohomology of the
Virasoro algebra with values in a tensor product of two braided vertex operator
algebras with complementary central charges . Each braided VOA is
constructed from the free Fock space realization of the Virasoro algebra with
an additional q-deformed harmonic oscillator degree of freedom. The braided VOA
structure arises from the theory of local systems over configuration spaces and
it yields an associative algebra structure on the cohomology. We explicitly
provide the four cohomology classes that serve as the generators of
and verify their relations. We also discuss the possible extensions of our
construction and its connection to the Liouville model and minimal string
theory.Comment: 50 pages, 7 figures, minor revisions, typos corrected, Communications
in Mathematical Physics, in pres
BRST Analysis of Physical States for 2D (Super) Gravity Coupled to (Super) Conformal Matter
We summarize some recent results on the BRST analysis of physical states of
2D gravity coupled to c<=1 conformal matter and the supersymmetric
generalization.Comment: 11 page
The BV-algebra structure of W_3 cohomology
We summarize some recent results obtained in collaboration with J. McCarthy
on the spectrum of physical states in gravity coupled to matter. We
show that the space of physical states, defined as a semi-infinite (or BRST)
cohomology of the algebra, carries the structure of a BV-algebra. This
BV-algebra has a quotient which is isomorphic to the BV-algebra of polyvector
fields on the base affine space of . Details have appeared elsewhere.
[Published in the proceedings of "Gursey Memorial Conference I: Strings and
Symmetries," Istanbul, June 1994, eds. G. Aktas et al., Lect. Notes in Phys.
447, (Springer Verlag, Berlin, 1995)]Comment: 8 pages; uses macros tables.tex and amssym.def (version 2.1 or later
Branes, Rings and Matrix Models in Minimal (Super)string Theory
We study both bosonic and supersymmetric (p,q) minimal models coupled to
Liouville theory using the ground ring and the various branes of the theory.
From the FZZT brane partition function, there emerges a unified, geometric
description of all these theories in terms of an auxiliary Riemann surface
M_{p,q} and the corresponding matrix model. In terms of this geometric
description, both the FZZT and ZZ branes correspond to line integrals of a
certain one-form on M_{p,q}. Moreover, we argue that there are a finite number
of distinct (m,n) ZZ branes, and we show that these ZZ branes are located at
the singularities of M_{p,q}. Finally, we discuss the possibility that the
bosonic and supersymmetric theories with (p,q) odd and relatively prime are
identical, as is suggested by the unified treatment of these models.Comment: 72 pages, 3 figures, improved treatment of FZZT and ZZ branes, minor
change
BRST Quantization of String Theory in AdS(3)
We study the BRST quantization of bosonic and NSR strings propagating in
AdS(3) x N backgrounds. The no-ghost theorem is proved using the
Frenkel-Garland-Zuckerman method. Regular and spectrally-flowed representations
of affine SL(2,R) appear on an equal footing. Possible generalizations to
related curved backgrounds are discussed.Comment: JHEP style, 23 pages; v2:minor changes and references added; v3:
typos corrected, version to appear in JHEP; v4: one reference adde
Lectures on BCOV holomorphic anomaly equations
The present article surveys some mathematical aspects of the BCOV holomorphic
anomaly equations introduced by Bershadsky, Cecotti, Ooguri and Vafa. It grew
from a series of lectures the authors gave at the Fields Institute in the
Thematic Program of Calabi-Yau Varieties in the fall of 2013.Comment: reference added, typos correcte
On the Crepant Resolution Conjecture in the Local Case
In this paper we analyze four examples of birational transformations between
local Calabi-Yau 3-folds: two crepant resolutions, a crepant partial
resolution, and a flop. We study the effect of these transformations on
genus-zero Gromov-Witten invariants, proving the
Coates-Corti-Iritani-Tseng/Ruan form of the Crepant Resolution Conjecture in
each case. Our results suggest that this form of the Crepant Resolution
Conjecture may also hold for more general crepant birational transformations.
They also suggest that Ruan's original Crepant Resolution Conjecture should be
modified, by including appropriate "quantum corrections", and that there is no
straightforward generalization of either Ruan's original Conjecture or the
Cohomological Crepant Resolution Conjecture to the case of crepant partial
resolutions. Our methods are based on mirror symmetry for toric orbifolds.Comment: 27 pages. This is a substantially revised and shortened version of my
preprint "Wall-Crossings in Toric Gromov-Witten Theory II: Local Examples";
all results contained here are also proved there. To appear in Communications
in Mathematical Physic
Chiral de Rham complex on Riemannian manifolds and special holonomy
Interpreting the chiral de Rham complex (CDR) as a formal Hamiltonian
quantization of the supersymmetric non-linear sigma model, we suggest a setup
for the study of CDR on manifolds with special holonomy. We show how to
systematically construct global sections of CDR from differential forms, and
investigate the algebra of the sections corresponding to the covariantly
constant forms associated with the special holonomy. As a concrete example, we
construct two commuting copies of the Odake algebra (an extension of the N=2
superconformal algebra) on the space of global sections of CDR of a Calabi-Yau
threefold and conjecture similar results for G_2 manifolds. We also discuss
quasi-classical limits of these algebras.Comment: 49 pages, title changed, major rewrite with no changes in the main
theorems, published versio
The BRST quantization and the no-ghost theorem for AdS_3
In our previous papers, we prove the no-ghost theorem without light-cone
directions (hep-th/0005002, hep-th/0303051). We point out that our results are
valid for more general backgrounds. In particular, we prove the no-ghost
theorem for AdS_3 in the context of the BRST quantization (with the standard
restriction on the spin). We compare our BRST proof with the OCQ proof and
establish the BRST-OCQ equivalence for AdS_3. The key in both approaches lies
in the certain structure of the matter Hilbert space as a product of two Verma
modules. We also present the no-ghost theorem in the most general form.Comment: 22 pages, JHEP and AMS-LaTeX; v2 & 3: minor improvement