128 research outputs found
Dual WDVV Equations in N=2 Supersymmetric Yang-Mills Theory
This paper studies the dual form of Witten-Dijkgraaf-Verlinde-Verlinde (WDVV)
equations in N=2 supersymmetric Yang-Mills theory by applying a duality
transformation to WDVV equations. The dual WDVV equations called in this paper
are non-linear differential equations satisfied by dual prepotential and are
found to have the same form with the original WDVV equations. However, in
contrast with the case of weak coupling calculus, the perturbative part of dual
prepotential itself does not satisfy the dual WDVV equations. Nevertheless, it
is possible to show that the non-perturbative part of dual prepotential can be
determined from dual WDVV equations, provided the perturbative part is given.
As an example, the SU(4) case is presented. The non-perturbative dual
prepotential derived in this way is consistent to the dual prepotential
obtained by D'Hoker and Phong.Comment: misprints are corrected, revtex, 10 page
Instanton calculus in R-R background and the topological string
We study a system of fractional D3 and D(-1) branes in a Ramond-Ramond closed
string background and show that it describes the gauge instantons of N=2 super
Yang-Mills theory and their interactions with the graviphoton of N=2
supergravity. In particular, we analyze the instanton moduli space using string
theory methods and compute the prepotential of the effective gauge theory
exploiting the localization methods of the instanton calculus showing that this
leads to the same information given by the topological string. We also comment
on the relation between our approach and the so-called Omega-background.Comment: 38 pages, 2 figures, JHEP class (included); final version to be
pubished in JHE
Gauge theory, topological strings, and S-duality
We offer a derivation of the duality between the topological U(1) gauge
theory on a Calabi-Yau 3-fold and the topological A-model on the same manifold.
This duality was conjectured recently by Iqbal, Nekrasov, Okounkov, and Vafa.
We deduce it from the S-duality of the IIB superstring. We also argue that the
mirror version of this duality relates the topological B-model on a Calabi-Yau
3-fold and a topological sector of the Type IIA Little String Theory on the
same manifold.Comment: 9 pages, latex. v2: a footnote has been added. The footnote corrects
an inaccuracy in the original argument; the results are unchanged. v3:
exposition improve
Drinfeld-Manin Instanton and Its Noncommutative Generalization
The Drinfeld-Manin construction of U(N) instanton is reformulated in the ADHM
formulism, which gives explicit general solutions of the ADHM constraints for
U(N) (N>=2k-1) k-instantons. For the N<2k-1 case, implicit results are given
systematically as further constraints, which can be used to the collective
coordinate integral. We find that this formulism can be easily generalized to
the noncommutative case, where the explicit solutions are as well obtained.Comment: 17 pages, LaTeX, references added, mailing address added,
clarifications adde
Instantons on Quivers and Orientifolds
We compute the prepotential for gauge theories descending from
SYM via quiver projections and mass deformations.
This accounts for gauge theories with product gauge groups and bifundamental
matter. The case of massive orientifold gauge theories with gauge group SO/Sp
is also described. In the case with no gravitational corrections the results
are shown to be in agreement with Seiberg-Witten analysis and previous results
in the literature.Comment: 28 pages, revised version, references added, some typos correcte
A note on instanton counting for N=2 gauge theories with classical gauge groups
We study the prepotential of N=2 gauge theories using the instanton counting
techniques introduced by Nekrasov. For the SO theories without matter we find a
closed expression for the full prepotential and its string theory gravitational
corrections. For the more subtle case of Sp theories without matter we discuss
general features and compute the prepotential up to instanton number three. We
also briefly discuss SU theories with matter in the symmetric and antisymmetric
representations. We check all our results against the predictions of the
corresponding Seiberg-Witten geometries.Comment: 24 pages, LaTeX. v2: refs added. v3: typos correcte
Stringy Instantons in SU(N) N=2 Non-Conformal Gauge Theories
In this paper we explicitly obtain the leading corrections to the SU(N) N=2
prepotential due to stringy instantons both in flat space-time and in the
presence of a non-trivial graviphoton background field. We show that the
stringy corrections to the prepotential are expressible in terms of the
elementary symmetric polynomials. For N>2 the theory is not conformal; we
discuss the introduction of an explicit dependence on the string scale \alpha'
in the low-energy effective action through the stringy non-perturbative sector.Comment: 22 pages, 1 figur
Twisted supersymmetric 5D Yang-Mills theory and contact geometry
We extend the localization calculation of the 3D Chern-Simons partition
function over Seifert manifolds to an analogous calculation in five dimensions.
We construct a twisted version of N=1 supersymmetric Yang-Mills theory defined
on a circle bundle over a four dimensional symplectic manifold. The notion of
contact geometry plays a crucial role in the construction and we suggest a
generalization of the instanton equations to five dimensional contact
manifolds. Our main result is a calculation of the full perturbative partition
function on a five sphere for the twisted supersymmetric Yang-Mills theory with
different Chern-Simons couplings. The final answer is given in terms of a
matrix model. Our construction admits generalizations to higher dimensional
contact manifolds. This work is inspired by the work of Baulieu-Losev-Nekrasov
from the mid 90's, and in a way it is covariantization of their ideas for a
contact manifold.Comment: 28 pages; v2: minor mistake corrected; v3: matches published versio
Quasi-localized states on noncommutative solitons
We consider noncommutative gauge theories which have zero mass states
propagating along both commutative and noncommutative dimensions. Solitons in
these theories generically carry U(m) gauge group on their world-volume. From
the point of view of string theory, these solitons correspond to
``branes within branes''. We show that once the world-volume U(m) gauge
theory is in the Higgs phase, light states become quasi-localized, rather than
strictly localized on the soliton, i.e. they mix with light bulk modes and have
finite widths to escape into the noncommutative dimensions. At small values of
U(m) symmetry breaking parameters, these widths are small compared to the
corresponding masses. Explicit examples considered are adjoint scalar field in
the background of a noncommutative vortex in U(1)-Higgs theory, and gauge
fields in instanton backgrounds in pure gauge noncommutative theories.Comment: 27 pages, references and comments added, final version to appear in
JHE
Supersymmetric D-brane Bound States with B-field and Higher Dimensional Instantons on Noncommutative Geometry
We classify supersymmetric D0-Dp bound states with a non-zero B-field by
considering T-dualities of intersecting branes at angles. Especially, we find
that the D0-D8 system with the B-field preserves 1/16, 1/8 and 3/16 of
supercharges if the B-field satisfies the ``(anti-)self-dual'' condition in
dimension eight. The D0-branes in this system are described by eight
dimensional instantons on non-commutative R^8. We also discuss the extended
ADHM construction of the eight-dimensional instantons and its deformation by
the B-field. The modified ADHM equations admit a sort of the `fuzzy sphere'
(embeddings of SU(2)) solution.Comment: 20 pages, LaTeX file, typos corrected and references adde
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