1,269 research outputs found
Algebraic-geometrical formulation of two-dimensional quantum gravity
We find a volume form on moduli space of double punctured Riemann surfaces
whose integral satisfies the Painlev\'e I recursion relations of the genus
expansion of the specific heat of 2D gravity. This allows us to express the
asymptotic expansion of the specific heat as an integral on an infinite
dimensional moduli space in the spirit of Friedan-Shenker approach. We outline
a conjectural derivation of such recursion relations using the
Duistermaat-Heckman theorem.Comment: 10 pages, Latex fil
RG Flow Irreversibility, C-Theorem and Topological Nature of 4D N=2 SYM
We determine the exact beta function and a RG flow Lyapunov function for N=2
SYM with gauge group SU(n). It turns out that the classical discriminants of
the Seiberg-Witten curves determine the RG potential. The radial
irreversibility of the RG flow in the SU(2) case and the non-perturbative
identity relating the -modulus and the superconformal anomaly, indicate the
existence of a four dimensional analogue of the c-theorem for N=2 SYM which we
formulate for the full SU(n) theory. Our investigation provides further
evidence of the essentially topological nature of the theory.Comment: 9 pages, LaTeX file. Discussion on WDVV and integrability. References
added. Version published in PR
Mass Deformations of Super Yang-Mills Theories in D= 2+1, and Super-Membranes: A Note
Mass deformations of supersymmetric Yang-Mills theories in three spacetime
dimensions are considered. The gluons of the theories are made massive by the
inclusion of a non-local gauge and Poincare invariant mass term due to
Alexanian and Nair, while the matter fields are given standard Gaussian
mass-terms. It is shown that the dimensional reduction of such mass deformed
gauge theories defined on or produces matrix quantum
mechanics with massive spectra. In particular, all known massive matrix quantum
mechanical models obtained by the deformations of dimensional reductions of
minimal super Yang-Mills theories in diverse dimensions are shown also to arise
from the dimensional reductions of appropriate massive Yang-Mills theories in
three spacetime dimensions. Explicit formulae for the gauge theory actions are
provided.Comment: 20 Page
Taming open/closed string duality with a Losev trick
A target space string field theory formulation for open and closed B-model is
provided by giving a Batalin-Vilkovisky quantization of the holomorphic
Chern-Simons theory with off-shell gravity background. The target space
expression for the coefficients of the holomorphic anomaly equation for open
strings are obtained. Furthermore, open/closed string duality is proved from a
judicious integration over the open string fields. In particular, by
restriction to the case of independence on continuous open moduli, the shift
formulas of [7] are reproduced and shown therefore to encode the data of a
closed string dual.Comment: 22 pages, no figures; v.2 Refs. and a comment added
Nonperturbative Relations in N=2 SUSY Yang-Mills and WDVV equation
We find the nonperturbative relation between , the prepotential and the
vevs in supersymmetric Yang-Mills theories with
gauge group . Nonlinear differential equations for including
the Witten -- Dijkgraaf -- Verlinde -- Verlinde equation are obtained. This
indicates that SYM theories are essentially topological field theories
and that should be seen as low-energy limit of some topological string theory.
Furthermore, we construct relevant modular invariant quantities, derive
canonical relations between the periods and investigate the structure of the
beta function by giving its explicit form in the moduli coordinates. In doing
this we discuss the uniformization problem for the quantum moduli space. The
method we propose can be generalized to supersymmetric Yang-Mills
theories with higher rank gauge groups.Comment: 12 pages, LaTex. Expanded version. New results, corrections,
references and acknowledgements adde
The stringy instanton partition function
We perform an exact computation of the gauged linear sigma model associated to a D1-D5 brane system on a resolved A 1 singularity. This is accomplished via supersymmetric localization on the blown-up two-sphere. We show that in the blow-down limit the partition function reduces to the Nekrasov partition function evaluating the equivariant volume of the instanton moduli space. For finite radius we obtain a tower of world-sheet instanton corrections, that we identify with the equivariant Gromov-Witten invariants of the ADHM moduli space. We show that these corrections can be encoded in a deformation of the Seiberg-Witten prepotential. From the mathematical viewpoint, the D1-D5 system under study displays a twofold nature: the D1-branes viewpoint captures the equivariant quantum cohomology of the ADHM instanton moduli space in the Givental formalism, and the D5-branes viewpoint is related to higher rank equivariant Donaldson-Thomas invariants
Irregular singularities in Liouville theory
Motivated by problems arising in the study of N=2 supersymmetric gauge
theories we introduce and study irregular singularities in two-dimensional
conformal field theory, here Liouville theory. Irregular singularities are
associated to representations of the Virasoro algebra in which a subset of the
annihilation part of the algebra act diagonally. In this paper we define
natural bases for the space of conformal blocks in the presence of irregular
singularities, describe how to calculate their series expansions, and how such
conformal blocks can be constructed by some delicate limiting procedure from
ordinary conformal blocks. This leads us to a proposal for the structure
functions appearing in the decomposition of physical correlation functions with
irregular singularities into conformal blocks. Taken together, we get a precise
prediction for the partition functions of some Argyres-Douglas type theories on
the four-sphere.Comment: 84 pages, 6 figure
Polynomial Structure of the (Open) Topological String Partition Function
In this paper we show that the polynomial structure of the topological string
partition function found by Yamaguchi and Yau for the quintic holds for an
arbitrary Calabi-Yau manifold with any number of moduli. Furthermore, we
generalize these results to the open topological string partition function as
discussed recently by Walcher and reproduce his results for the real quintic.Comment: 15 page
Non-holomorphic terms in N=2 SUSY Wilsonian actions and RG equation
In this paper we first investigate the Ansatz of one of the present authors
for K(\Psi,\bar\Psi), the adimensional modular invariant non-holomorphic
correction to the Wilsonian effective Lagrangian of an N=2 globally
supersymmetric gauge theory. The renormalisation group beta-function of the
theory crucially allows us to express K(\Psi,\bar\Psi) in a form that easily
generalises to the case in which the theory is coupled to N_F hypermultiplets
in the fundamental representation of the gauge group. This function satisfies
an equation which should be viewed as a fully non-perturbative ``non-chiral
superconformal Ward identity". We also determine its renormalisation group
equation. Furthermore, as a first step towards checking the validity of this
Ansatz, we compute the contribution to K(\Psi,\bar\Psi) from instantons of
winding number k=1 and k=2. As a by-product of our analysis we check a
non-renormalisation theorem for N_F=4.Comment: 39 pages, LaTex file, no figure
Partonic description of a supersymmetric p-brane
We consider supersymmetric extensions of a recently proposed partonic
description of a bosonic p-brane which reformulates the Nambu-Goto action as an
interacting multi-particle action with Filippov-Lie algebra gauge symmetry. We
construct a worldline supersymmetric action by postulating, among others, a
p-form fermion. Demanding a local worldline supersymmetry rather than the full
worldvolume supersymmetry, we circumvent a known no-go theorem against the
construction of a Ramond-Neveu-Schwarz supersymmetric action for a p-brane of
p>1. We also derive a spacetime supersymmetric Green-Schwarz extension from the
preexisting kappa-symmetric action.Comment: 1+16 pages, no figure; References added and Concluding section
expanded. Final version to appear in JHE
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