1,145 research outputs found
Sasaki-Einstein Manifolds
This article is an overview of some of the remarkable progress that has been
made in Sasaki-Einstein geometry over the last decade, which includes a number
of new methods of constructing Sasaki-Einstein manifolds and obstructions.Comment: 58 pages. Invited contribution to Surveys in Differential Geometry.
v2: references and discussion adde
Global Worldsheet Anomalies from M-Theory
We present an M-theory proof of the anomaly of Freed and Witten which in
general shifts the quantisation law for the U(1) gauge field on a D6-brane. The
derivation requires an understanding of how fields on the D6-brane lift to
M-theory, together with a localisation formula which we prove using a
U(1)-index theorem. We also show how the anomaly is related to the K-theory
classification of Ramond-Ramond fields. In addition we discuss the M-theory
origin of the D6-brane effective action, and illustrate the general arguments
with a concrete example.Comment: 25 pages; v2: minor alterations, references added; v3: various
arguments clarified, mathematical background added. Published versio
Symmetry-breaking vacua and baryon condensates in AdS/CFT
We study the gravity duals of symmetry-breaking deformations of
superconformal field theories, AdS/CFT dual to Type IIB string theory on AdS_5
x Y where Y is a Sasaki-Einstein manifold. In these vacua both conformal
invariance and baryonic symmetries are spontaneously broken. We present a
detailed discussion of the supergravity moduli space, which involves flat form
fields on asymptotically conical Calabi-Yau manifolds, and match this to the
gauge theory vacuum moduli space. We discuss certain linearised fluctuations of
the moduli, identifying the Goldstone bosons associated with spontaneous
breaking of non-anomalous baryonic symmetries. The remaining moduli fields are
related to spontaneous breaking of anomalous baryonic symmetries. We also
elaborate on the proposal that computing condensates of baryon operators is
equivalent to computing the partition function of a non-compact Euclidean
D3-brane in the background supergravity solution, with fixed boundary
conditions at infinity.Comment: 121 pages; v2: references adde
D2-brane Chern-Simons theories: F-maximization = a-maximization
We study a system of N D2-branes probing a generic Calabi-Yau three-fold
singularity in the presence of a non-zero quantized Romans mass n. We argue
that the low-energy effective N = 2 Chern-Simons quiver gauge theory flows to a
superconformal fixed point in the IR, and construct the dual AdS_4 solution in
massive IIA supergravity. We compute the free energy F of the gauge theory on
S^3 using localization. In the large N limit we find F = c(nN)^{1/3}a^{2/3},
where c is a universal constant and a is the a-function of the "parent"
four-dimensional N = 1 theory on N D3-branes probing the same Calabi-Yau
singularity. It follows that maximizing F over the space of admissible
R-symmetries is equivalent to maximizing a for this class of theories.
Moreover, we show that the gauge theory result precisely matches the
holographic free energy of the supergravity solution, and provide a similar
matching of the VEV of a BPS Wilson loop operator.Comment: 19 pages; v2: minor correction
The character of the supersymmetric Casimir energy
We study the supersymmetric Casimir energy of
field theories with an R-symmetry, defined on rigid
supersymmetric backgrounds , using a Hamiltonian formalism.
These backgrounds admit an ambi-Hermitian geometry, and we show that the net
contributions to arise from certain twisted holomorphic modes
on , with respect to both complex structures. The
supersymmetric Casimir energy may then be identified as a limit of an
index-character that counts these modes. In particular this explains a recent
observation relating on to the anomaly
polynomial. As further applications we compute for certain
secondary Hopf surfaces, and discuss how the index-character may also be used
to compute generalized supersymmetric indices.Comment: 47 pages; v2: footnote 6 added, formula (5.29) changed, Section 6
moved to Appendix
Baryonic branches and resolutions of Ricci-flat Kahler cones
We consider deformations of N=1 superconformal field theories that are
AdS/CFT dual to Type IIB string theory on Sasaki-Einstein manifolds,
characterised by non-zero vacuum expectation values for certain baryonic
operators. Such baryonic branches are constructed from (partially) resolved,
asymptotically conical Ricci-flat Kahler manifolds, together with a choice of
point where the stack of D3-branes is placed. The complete solution then
describes a renormalisation group flow between two AdS fixed points. We discuss
the use of probe Euclidean D3-branes in these backgrounds as a means to compute
expectation values of baryonic operators. The Y^{p,q} theories are used as
illustrative examples throughout the paper. In particular, we present
supergravity solutions describing flows from the Y^{p,q} theories to various
different orbifold field theories in the infra-red, and successfully match this
to an explicit field theory analysis.Comment: 51 pages, v2: reference added and minor changes; v3: minor changes,
published versio
The large N limit of quiver matrix models and Sasaki-Einstein manifolds
We study the matrix models that result from localization of the partition
functions of N=2 Chern-Simons-matter theories on the three-sphere. A large
class of such theories are conjectured to be holographically dual to M-theory
on Sasaki-Einstein seven-manifolds. We study the M-theory limit (large N and
fixed Chern-Simons levels) of these matrix models for various examples, and
show that in this limit the free energy reproduces the expected AdS/CFT result
of N^{3/2}/Vol(Y)^{1/2}, where Vol(Y) is the volume of the corresponding
Sasaki-Einstein metric. More generally we conjecture a relation between the
large N limit of the partition function, interpreted as a function of trial
R-charges, and the volumes of Sasakian metrics on links of Calabi-Yau four-fold
singularities. We verify this conjecture for a family of U(N)^2 Chern-Simons
quivers based on M2 branes at hypersurface singularities, and for a U(N)^3
theory based on M2 branes at a toric singularity.Comment: 38 pages, 4 figures; v2: minor changes, typos and factor of 2 in eq.
(5.19) fixed, references and 2 figures added; v3: new section 4.5 added; v4:
more typos fixed, range of validity of (4.19) clarifie
Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
Recently an infinite family of explicit Sasaki-Einstein metrics Y^{p,q} on
S^2 x S^3 has been discovered, where p and q are two coprime positive integers,
with q<p. These give rise to a corresponding family of Calabi-Yau cones, which
moreover are toric. Aided by several recent results in toric geometry, we show
that these are Kahler quotients C^4//U(1), namely the vacua of gauged linear
sigma models with charges (p,p,-p+q,-p-q), thereby generalising the conifold,
which is p=1,q=0. We present the corresponding toric diagrams and show that
these may be embedded in the toric diagram for the orbifold C^3/Z_{p+1}xZ_{p+1}
for all q<p with fixed p. We hence find that the Y^{p,q} manifolds are AdS/CFT
dual to an infinite class of N=1 superconformal field theories arising as IR
fixed points of toric quiver gauge theories with gauge group SU(N)^{2p}. As a
non-trivial example, we show that Y^{2,1} is an explicit irregular
Sasaki-Einstein metric on the horizon of the complex cone over the first del
Pezzo surface. The dual quiver gauge theory has already been constructed for
this case and hence we can predict the exact central charge of this theory at
its IR fixed point using the AdS/CFT correspondence. The value we obtain is a
quadratic irrational number and, remarkably, agrees with a recent purely field
theoretic calculation using a-maximisation.Comment: 54 pages, 5 figures; minor changes; further minor changes, ref [8]
added - published version; eqns 1.3, 1.4 remove
The supersymmetric NUTs and bolts of holography
We show that a given conformal boundary can have a rich and intricate space
of supersymmetric supergravity solutions filling it, focusing on the case where
this conformal boundary is a biaxially squashed Lens space. Generically we find
that the biaxially squashed Lens space S^3/Z_p admits Taub-NUT-AdS fillings,
with topology R^4/Z_p, as well as smooth Taub-Bolt-AdS fillings with
non-trivial topology. We show that the Taub-NUT-AdS solutions always lift to
solutions of M-theory, and correspondingly that the gravitational free energy
then agrees with the large N limit of the dual field theory free energy,
obtained from the localized partition function of a class of N=2
Chern-Simons-matter theories. However, the solutions of Taub-Bolt-AdS type only
lift to M-theory for appropriate classes of internal manifold, meaning that
these solutions exist only for corresponding classes of three-dimensional N=2
field theories.Comment: 54 pages plus 7 appendices; v2: discussion of global properties of
gauge field A in eleven dimensions improved and some parts of the paper
rewritten to reflect this, new subsections 6.4.1, 6.4.2 and appendix F added,
references added; v3: final version published in Nuclear Physics
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