59 research outputs found
Multi-Instanton Calculus and the AdS/CFT Correspondence in N=4 Superconformal Field Theory
We present a self-contained study of ADHM multi-instantons in SU(N) gauge theory, especially the novel interplay with supersymmetry and the large-N limit. We give both field- and string-theoretic derivations of the N=4 supersymmetric multi-instanton action and collective coordinate integration measure. As a central application, we focus on certain n-point functions G_n, n=16, 8 or 4, in N=4 SU(N) gauge theory at the conformal point (as well as on related higher-partial-wave correlators); these are correlators in which the 16 exact supersymmetric and superconformal fermion zero modes are saturated. In the large-N limit, for the first time in any 4-dimensional theory, we are able to evaluate all leading-order multi-instanton contributions exactly. We find compelling evidence for Maldacena's conjecture: (1) The large-N k-instanton collective coordinate space has the geometry of a single copy of AdS_5 x S^5. (2) The integration measure on this space includes the partition function of 10-dimensional N=1 SU(k) gauge theory dimensionally reduced to 0 dimensions, matching the description of D-instantons in Type IIB string theory. (3) In exact agreement with Type IIB string calculations, at the k-instanton level, G_n = \sqrt{N} g^8 k^{n-7/2} e^{2\pi ik\tau} \sum_{d|k} d^{-2} F_n(x_1,...,x_n), where F_n is identical to a convolution of n bulk-to-boundary supergravity propagators
D-instantons and twistors: some exact results
We present some results on instanton corrections to the hypermultiplet moduli
space in Calabi-Yau compactifications of Type II string theories. Previously,
using twistor methods, only a class of D-instantons (D2-instantons wrapping
A-cycles) was incorporated exactly and the rest was treated only linearly. We
go beyond the linear approximation and give a set of holomorphic functions
which, through a known procedure, capture the effect of D-instantons at all
orders. Moreover, we show that for a sector where all instanton charges have
vanishing symplectic invariant scalar product, the hypermultiplet metric can be
computed explicitly.Comment: 32 pages, 3 figures, uses JHEP3.cls; some changes in section 3.3.3;
corrected formula for the contact potentia
Instantons in the Double-Tensor Multiplet
The double-tensor multiplet naturally appears in type IIB superstring
compactifications on Calabi-Yau threefolds, and is dual to the universal
hypermultiplet. We revisit the calculation of instanton corrections to the
low-energy effective action, in the supergravity approximation. We derive a
Bogomolny'i bound for the double-tensor multiplet and find new instanton
solutions saturating the bound. They are characterized by the topological
charges and the asymptotic values of the scalar fields in the double-tensor
multiplet.Comment: 17 pages, LaTeX2e with amsmath.sty; v2: minor change
N=2 supergravity in five dimensions revisited
We construct matter-coupled N=2 supergravity in five dimensions, using the
superconformal approach. For the matter sector we take an arbitrary number of
vector-, tensor- and hyper-multiplets. By allowing off-diagonal vector-tensor
couplings we find more general results than currently known in the literature.
Our results provide the appropriate starting point for a systematic search for
BPS solutions, and for applications of M-theory compactifications on Calabi-Yau
manifolds with fluxes.Comment: 35 pages; v.2: A sign changed in a bilinear fermion term in (5.7
On NS5-brane instantons and volume stabilization
We study general aspects of NS5-brane instantons in relation to the
stabilization of the volume modulus in Calabi-Yau compactifications of type II
strings with fluxes, and their orientifold versions. These instantons correct
the Kahler potential and generically yield significant contributions to the
scalar potential at intermediate values of string coupling constant and volume.
Under suitable conditions they yield uplifting terms that allow for
meta--stable de Sitter vacua.Comment: 29 pages, 3 figures; statements about fields G^a made more precise,
added some clarifications, typos correcte
Generalized instantons in N = 4 super Yang-Mills theory and spinorial geometry
Using spinorial geometry techniques, we classify the supersymmetric solutions
of euclidean super Yang-Mills theory. These backgrounds represent
generalizations of instantons with nontrivial scalar fields turned on, and
satisfy some constraints that bear a similarity with the Hitchin equations, and
contain the Donaldson equations as a special subcase. It turns out that these
constraints can be obtained by dimensional reduction of the octonionic
instanton equations, and may be rephrased in terms of a selfduality-like
condition for a complex connection. We also show that the supersymmetry
conditions imply the equations of motion only partially.Comment: 29 pages, 3 tables. v2: references added. v3: conclusion extended,
version published in JHE
Scherk-Schwarz Reduction of D=5 Special and Quaternionic Geometry
We give the N=2 gauged supergravity interpretation of a generic D=4, N=2
theory as it comes from generalized Scherk-Schwarz reduction of D=5, N=2
(ungauged) supergravity. We focus on the geometric aspects of the D=4 data such
as the general form of the scalar potential and masses in terms of the gauging
of a ``flat group''. Higgs and super-Higgs mechanism are discussed in some
detail.Comment: final version to be published on Class.Quant.Gra
Membrane Instantons and de Sitter Vacua
We investigate membrane instanton effects in type IIA strings compactified on
rigid Calabi-Yau manifolds. These effects contribute to the low-energy
effective action of the universal hypermultiplet. In the absence of additional
fivebrane instantons, the quaternionic geometry of this hypermultiplet is
determined by solutions of the three-dimensional Toda equation. We construct
solutions describing membrane instantons, and find perfect agreement with the
string theory prediction. In the context of flux compactifications we discuss
how membrane instantons contribute to the scalar potential and the
stabilization of moduli. Finally, we demonstrate the existence of meta-stable
de Sitter vacua.Comment: v3: minor clarifications, JHEP version, 38 page
Twistors and Black Holes
Motivated by black hole physics in N=2, D=4 supergravity, we study the
geometry of quaternionic-Kahler manifolds M obtained by the c-map construction
from projective special Kahler manifolds M_s. Improving on earlier treatments,
we compute the Kahler potentials on the twistor space Z and Swann space S in
the complex coordinates adapted to the Heisenberg symmetries. The results bear
a simple relation to the Hesse potential \Sigma of the special Kahler manifold
M_s, and hence to the Bekenstein-Hawking entropy for BPS black holes. We
explicitly construct the ``covariant c-map'' and the ``twistor map'', which
relate real coordinates on M x CP^1 (resp. M x R^4/Z_2) to complex coordinates
on Z (resp. S). As applications, we solve for the general BPS geodesic motion
on M, and provide explicit integral formulae for the quaternionic Penrose
transform relating elements of H^1(Z,O(-k)) to massless fields on M annihilated
by first or second order differential operators. Finally, we compute the exact
radial wave function (in the supergravity approximation) for BPS black holes
with fixed electric and magnetic charges.Comment: 47 pages, v2: typos corrected, reference added, v3: minor change
Topological A-Type Models with Flux
We study deformations of the A-model in the presence of fluxes, by which we
mean rank-three tensors with antisymmetrized upper/lower indices, using the
AKSZ construction. Generically these are topological membrane models, and we
show that the fluxes are related to deformations of the Courant bracket which
generalize the twist by a closed 3-from , in the sense that satisfying the
AKSZ master equation implies the integrability conditions for an almost
generalized complex structure with respect to the deformed Courant bracket. In
addition, the master equation imposes conditions on the fluxes that generalize
. The membrane model can be defined on a large class of - and -structure manifolds, including geometries inspired by
supersymmetric -models with additional supersymmetries due to almost
complex (but not necessarily complex) structures in the target space.
Furthermore, we show that the model can be defined on three particular
half-flat manifolds related to the Iwasawa manifold.
When only -flux is turned on it is possible to obtain a topological string
model, which we do for the case of a Calabi-Yau with a closed 3-form turned on.
The simplest deformation from the A-model is due to the
component of a non-trivial -field. The model is generically no longer
evaluated on holomorphic maps and defines new topological invariants.
Deformations due to -flux can be more radical, completely preventing
auxiliary fields from being integrated out.Comment: 30 pages. v2: Improved Version. References added. v3: Minor changes,
published in JHE
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