81 research outputs found
On Berenstein-Douglas-Seiberg Duality
I review the proposal of Berenstein-Douglas for a completely general
definition of Seiberg duality. To give evidence for their conjecture I present
the first example of a physical dual pair and explicitly check that it
satisfies the requirements. Then I explicitly show that a pair of toric dual
quivers is also dual according to their proposal. All these computations go
beyond tilting modules, and really work in the derived category. I introduce
all necessary mathematics where needed.Comment: 22 pages, LaTe
Supersymmetric States in M5/M2 CFTs
We propose an exact, finite formula for the partition function over
BPS states in the conformal field theory on the world volume of
coincident M5 branes and BPS states in the theory of coincident
M2 branes. We obtain our partition function by performing the radial
quantization of the Coulomb Branches of these theories, and rederive the same
formula from the quantization of supersymmetric giant and dual giant gravitons
in and . Our partition function is
qualitatively similar to the analogous quantity in Yang Mills. It
reduces to the sum over supersymmetric multi gravitons at low energies, but
deviates from this supergravity formula at energies that scale like a positive
power of .Comment: 24 pages, harvmac; v2 reference adde
Dual giant gravitons in AdS Y (Sasaki-Einstein)
We consider BPS motion of dual giant gravitons on Ad where
represents a five-dimensional Sasaki-Einstein manifold. We find that the
phase space for the BPS dual giant gravitons is symplectically isomorphic to
the Calabi-Yau cone over , with the K\"{a}hler form identified with the
symplectic form. The quantization of the dual giants therefore coincides with
the K\"{a}hler quantization of the cone which leads to an explicit
correspondence between holomorphic wavefunctions of dual giants and
gauge-invariant operators of the boundary theory. We extend the discussion to
dual giants in where is a seven-dimensional
Sasaki-Einstein manifold; for special motions the phase space of the dual
giants is symplectically isomorphic to the eight-dimensional Calabi-Yau cone.Comment: 14 pages. (v2) typo's corrected; factors of AdS radius reinstated for
clarity; remarks about dual giant wavefunctions in T^{1,1} expanded and put
in a new subsectio
The Toric Phases of the Y^{p,q} Quivers
We construct all connected toric phases of the recently discovered
quivers and show their IR equivalence using Seiberg duality. We also compute
the R and global U(1) charges for a generic toric phase of .Comment: 14 pages, 3 figure
Reverse geometric engineering of singularities
One can geometrically engineer supersymmetric field theories theories by
placing D-branes at or near singularities. The opposite process is described,
where one can reconstruct the singularities from quiver theories. The
description is in terms of a noncommutative quiver algebra which is constructed
from the quiver diagram and the superpotential. The center of this
noncommutative algebra is a commutative algebra, which is the ring of
holomorphic functions on a variety V. If certain algebraic conditions are met,
then the reverse geometric engineering produces V as the geometry that D-branes
probe. It is also argued that the identification of V is invariant under
Seiberg dualities.Comment: 17 pages, Latex. v2: updates reference
Dibaryon Spectroscopy
The AdS/CFT correspondence relates dibaryons in superconformal gauge theories
to holomorphic curves in Kaehler-Einstein surfaces. The degree of the
holomorphic curves is proportional to the gauge theory conformal dimension of
the dibaryons. Moreover, the number of holomorphic curves should match, in an
appropriately defined sense, the number of dibaryons. Using AdS/CFT backgrounds
built from the generalized conifolds of Gubser, Shatashvili, and Nekrasov
(1999), we show that the gauge theory prediction for the dimension of
dibaryonic operators does indeed match the degree of the corresponding
holomorphic curves. For AdS/CFT backgrounds built from cones over del Pezzo
surfaces, we are able to match the degree of the curves to the conformal
dimension of dibaryons for the n'th del Pezzo surface, n=1,2,...,6. Also, for
the del Pezzos and the A_k type generalized conifolds, for the dibaryons of
smallest conformal dimension, we are able to match the number of holomorphic
curves with the number of possible dibaryon operators from gauge theory.Comment: 30 pages, 6 figures, corrected refs; v3 typos correcte
Dibaryons from Exceptional Collections
We discuss aspects of the dictionary between brane configurations in del
Pezzo geometries and dibaryons in the dual superconformal quiver gauge
theories. The basis of fractional branes defining the quiver theory at the
singularity has a K-theoretic dual exceptional collection of bundles which can
be used to read off the spectrum of dibaryons in the weakly curved dual
geometry. Our prescription identifies the R-charge R and all baryonic U(1)
charges Q_I with divisors in the del Pezzo surface without any Weyl group
ambiguity. As one application of the correspondence, we identify the cubic
anomaly tr R Q_I Q_J as an intersection product for dibaryon charges in large-N
superconformal gauge theories. Examples can be given for all del Pezzo surfaces
using three- and four-block exceptional collections. Markov-type equations
enforce consistency among anomaly equations for three-block collections.Comment: 47 pages, 11 figures, corrected ref
"Holey Sheets" - Pfaffians and Subdeterminants as D-brane Operators in Large N Gauge Theories
In the AdS/CFT correspondence, wrapped D3-branes (such as "giant gravitons")
on the string theory side of the correspondence have been identified with
Pfaffian, determinant and subdeterminant operators on the field theory side. We
substantiate this identification by showing that the presence of pairs of such
operators in a correlation function of a large N gauge theory naturally leads
to a modified 't Hooft expansion including also worldsheets with boundaries.
This happens independently of supersymmetry or conformal invariance.Comment: 39 pages, 10 figures, harvma
Counting 1/8-BPS Dual-Giants
We count 1/8-BPS states in type IIB string theory on AdS_5 x S^5 background
which carry three independent angular momenta on S^5. These states can be
counted by considering configurations of multiple dual-giant gravitons up to N
in number which share at least four supersymmetries. We map this counting
problem to that of counting the energy eigen states of a system of N bosons in
a 3-dimensional harmonic oscillator. We also count 1/8-BPS states with two
independent non-zero spins in AdS_5 and one non-zero angular momentum on S^5 by
considering configurations of arbitrary number of giant gravitons that share at
least four supersymmetries.Comment: 19 page
Exceptional Collections and del Pezzo Gauge Theories
Stacks of D3-branes placed at the tip of a cone over a del Pezzo surface
provide a way of geometrically engineering a small but rich class of
gauge/gravity dualities. We develop tools for understanding the resulting
quiver gauge theories using exceptional collections. We prove two important
results for a general quiver gauge theory: 1) we show the ordering of the nodes
can be determined up to cyclic permutation and 2) we derive a simple formula
for the ranks of the gauge groups (at the conformal point) in terms of the
numbers of bifundamentals. We also provide a detailed analysis of four node
quivers, examining when precisely mutations of the exceptional collection are
related to Seiberg duality.Comment: 26 pages, 1 figure; v2 footnote 2 amended; v3 ref adde
- …