504 research outputs found
Seiberg-Witten prepotential for E-string theory and random partitions
We find a Nekrasov-type expression for the Seiberg-Witten prepotential for
the six-dimensional non-critical E_8 string theory toroidally compactified down
to four dimensions. The prepotential represents the BPS partition function of
the E_8 strings wound around one of the circles of the toroidal
compactification with general winding numbers and momenta. We show that our
expression exhibits expected modular properties. In particular, we prove that
it obeys the modular anomaly equation known to be satisfied by the
prepotential.Comment: 14 page
Ground States of S-duality Twisted N=4 Super Yang-Mills Theory
We study the low-energy limit of a compactification of N=4 U(n) super
Yang-Mills theory on with boundary conditions modified by an S-duality
and R-symmetry twist. This theory has N=6 supersymmetry in 2+1D. We analyze the
compactification of this 2+1D theory by identifying a dual weakly coupled
type-IIA background. The Hilbert space of normalizable ground states is
finite-dimensional and appears to exhibit a rich structure of sectors. We
identify most of them with Hilbert spaces of Chern-Simons theory (with
appropriate gauge groups and levels). We also discuss a realization of a
related twisted compactification in terms of the (2,0)-theory, where the recent
solution by Gaiotto and Witten of the boundary conditions describing D3-branes
ending on a (p,q) 5-brane plays a crucial role.Comment: 104 pages, 5 figures. Revisions to subsection (6.6) and other minor
corrections included in version
The non-Abelian tensor multiplet in loop space
We introduce a non-Abelian tensor multiplet directly in the loop space
associated with flat six-dimensional Minkowski space-time, and derive the
supersymmetry variations for on-shell supersymmetry.Comment: 11 pages, v2: cleaner presentation, mistakes are corrected (and an
erroneous section was removed
On Communication Complexity of Fixed Point Computation
Brouwer's fixed point theorem states that any continuous function from a
compact convex space to itself has a fixed point. Roughgarden and Weinstein
(FOCS 2016) initiated the study of fixed point computation in the two-player
communication model, where each player gets a function from to
, and their goal is to find an approximate fixed point of the
composition of the two functions. They left it as an open question to show a
lower bound of for the (randomized) communication complexity of
this problem, in the range of parameters which make it a total search problem.
We answer this question affirmatively.
Additionally, we introduce two natural fixed point problems in the two-player
communication model.
Each player is given a function from to ,
and their goal is to find an approximate fixed point of the concatenation of
the functions.
Each player is given a function from to , and
their goal is to find an approximate fixed point of the interpolation of the
functions.
We show a randomized communication complexity lower bound of
for these problems (for some constant approximation factor).
Finally, we initiate the study of finding a panchromatic simplex in a
Sperner-coloring of a triangulation (guaranteed by Sperner's lemma) in the
two-player communication model: A triangulation of the -simplex is
publicly known and one player is given a set and a coloring
function from to , and the other player is given a set
and a coloring function from to ,
such that , and their goal is to find a panchromatic
simplex. We show a randomized communication complexity lower bound of
for the aforementioned problem as well (when is large)
Seiberg-Witten prepotential for E-string theory and global symmetries
We obtain Nekrasov-type expressions for the Seiberg-Witten prepotential for
the six-dimensional (1,0) supersymmetric E-string theory compactified on T^2
with nontrivial Wilson lines. We consider compactification with four general
Wilson line parameters, which partially break the E_8 global symmetry. In
particular, we investigate in detail the cases where the Lie algebra of the
unbroken global symmetry is E_n + A_{8-n} with n=8,7,6,5 or D_8. All our
Nekrasov-type expressions can be viewed as special cases of the elliptic
analogue of the Nekrasov partition function for the SU(N) gauge theory with
N_f=2N flavors. We also present a new expression for the Seiberg-Witten curve
for the E-string theory with four Wilson line parameters, clarifying the
connection between the E-string theory and the SU(2) Seiberg-Witten theory with
N_f=4 flavors.Comment: 22 pages. v2: comments and a reference added, version to appear in
JHE
Towards Deconstruction of the Type D (2,0) Theory
We propose a four-dimensional supersymmetric theory that deconstructs, in a
particular limit, the six-dimensional theory of type . This 4d
theory is defined by a necklace quiver with alternating gauge nodes
and . We test this proposal by comparing the
6d half-BPS index to the Higgs branch Hilbert series of the 4d theory. In the
process, we overcome several technical difficulties, such as Hilbert series
calculations for non-complete intersections, and the choice of
versus gauge groups. Consistently, the result matches the Coulomb
branch formula for the mirror theory upon reduction to 3d
Wilson loops in large N field theories
We propose a method to calculate the expectation values of an operator
similar to the Wilson loop in the large N limit of field theories. We consider
N=4 3+1 dimensional super-Yang-Mills. The prescription involves calculating the
area of a fundamental string worldsheet in certain supergravity backgrounds. We
also consider the case of coincident M-theory fivebranes where one is lead to
calculating the area of M-theory two-branes. We briefly discuss the computation
for 2+1 dimensional super-Yang-Mills with sixteen supercharges which is
non-conformal. In all these cases we calculate the energy of quark-antiquark
pair.Comment: 12 pages, harvmac. v2: sign in eqn. (5.6) corrected, v3 typo
correcte
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