2,608 research outputs found
Master Partitions for Large N Matrix Field Theories
We introduce a systematic approach for treating the large N limit of matrix
field theories.Comment: 11 pages, LaTeX, REVTE
Bulk Witten Indices and the Number of Normalizable Ground States in Supersymmetric Quantum Mechanics of Orthogonal, Symplectic and Exceptional Groups
This note addresses the question of the number of normalizable vacuum states
in supersymmetric quantum mechanics with sixteen supercharges and arbitrary
semi-simple compact gauge group, up to rank three. After evaluating certain
contour integrals obtained by appropriately adapting BRST deformation
techniques we propose novel rational values for the bulk indices. Our results
demonstrate that an asymptotic method for obtaining the boundary contribution
to the index, originally due to Green and Gutperle, fails for groups other than
SU(N). We then obtain likely values for the number of ground states of these
systems. In the case of orthogonal and symplectic groups our finding is
consistent with recent conjectures of Kac and Smilga, but appears to contradict
their result in the case of the exceptional group G_2.Comment: 7 pages, one comment plus reference added, version to be published in
Phys. Lett.
Finite Yang-Mills Integrals
We use Monte Carlo methods to directly evaluate D-dimensional SU(N)
Yang-Mills partition functions reduced to zero Euclidean dimensions, with and
without supersymmetry. In the non-supersymmetric case, we find that the
integrals exist for D=3, N>3 and D=4, N>2 and, lastly, D >= 5, N >= 2. We
conclude that the D=3 and D=4 integrals exist in the large N limit, and
therefore lead to a well-defined, new type of Eguchi-Kawai reduced gauge
theory. For the supersymmetric case, we check, up to SU(5), recently proposed
exact formulas for the D=4 and D=6 D-instanton integrals, including the
explicit form of the normalization factor needed to interpret the integrals as
the bulk contribution to the Witten index.Comment: 7 pages, LaTeX, REVTE
Grassmannian Integrals in Minkowski Signature, Amplitudes, and Integrability
We attempt to systematically derive tree-level scattering amplitudes in
four-dimensional, planar, maximally supersymmetric Yang-Mills theory from
integrability. We first review the connections between integrable spin chains,
Yangian invariance, and the construction of such invariants in terms of
Grassmannian contour integrals. Building upon these results, we equip a class
of Grassmannian integrals for general symmetry algebras with unitary
integration contours. These contours emerge naturally by paying special
attention to the proper reality conditions of the algebras. Specializing to
psu(2,2|4) and thus to maximal superconformal symmetry in Minkowski space, we
find in a number of examples expressions similar to, but subtly different from
the perturbative physical scattering amplitudes. Our results suggest a subtle
breaking of Yangian invariance for the latter, with curious implications for
their construction from integrability.Comment: 44 pages, 2 figures; v2: published version, minor change
Two-loop commuting charges and the string/gauge duality
We briefly review the status quo of the application of integrable systems
techniques to the AdS/CFT correspondence in the large charge approximation, a
rapidly evolving topic. Intricate string and gauge computations of,
respectively, energies and scaling dimensions agree at the one and two-loop
level, but disagree starting from three loops. To add to this pattern, we
present further computations which demonstrate that for folded and circular
spinning strings the full tower of infinitely many hidden commuting charges,
responsible for the integrability, also agrees up to two, but not three, loops.Comment: 12 pages, Latex, contribution to 5th International Workshop on Lie
Theory and Its Applications in Physics, Varna, Bulgaria, 16-22 Jun 2003; v2:
references adde
Planar N=4 gauge theory and the Inozemtsev long range spin chain
We investigate whether the (planar, two complex scalar) dilatation operator
of N=4 gauge theory can be, perturbatively and, perhaps, non-perturbatively,
described by an integrable long range spin chain with elliptic exchange
interaction. Such a chain was introduced some time ago by Inozemtsev. In the
limit of sufficiently ``long'' operators a Bethe ansatz exists, which we apply
at the perturbative two- and three-loop level. Spectacular agreement is found
with spinning string predictions of Frolov and Tseytlin for the two-loop
energies of certain large charge operators. However, we then go on to show that
the agreement between perturbative gauge theory and semi-classical string
theory begins to break down, in a subtle fashion, at the three-loop level. This
corroborates a recently found disagreement between three-loop gauge theory and
near plane-wave string theory results, and quantitatively explains a previously
obtained puzzling deviation between the string proposal and a numerical
extrapolation of finite size three-loop anomalous dimensions. At four loops and
beyond, we find that the Inozemtsev chain exhibits a generic breakdown of
perturbative BMN scaling. However, our proposal is not necessarily limited to
perturbation theory, and one would hope that the string theory results can be
recovered from the Inozemtsev chain at strong 't Hooft coupling.Comment: 31 pages, no figure; v1: one reference added, minor changes; v2:
slightly extended discussion of rapidity, references adde
Statistical Physics Approach to M-theory Integrals
We explain the concepts of computational statistical physics which have
proven very helpful in the study of Yang-Mills integrals, an ubiquitous new
class of matrix models. Issues treated are: Absolute convergence versus Monte
Carlo computability of near-singular integrals, singularity detection by
Markov-chain methods, applications to asymptotic eigenvalue distributions and
to numerical evaluations of multiple bosonic and supersymmetric integrals. In
many cases already, it has been possible to resolve controversies between
conflicting analytical results using the methods presented here.Comment: 6 pages, talk presented by WK at conference 'Non- perturbative
Quantum Effects 2000', Paris, Sept 200
Limiting Geometries of Two Circular Maldacena-Wilson Loop Operators
We further analyze a recent perturbative two-loop calculation of the
expectation value of two axi-symmetric circular Maldacena-Wilson loops in N=4
gauge theory. Firstly, it is demonstrated how to adapt the previous calculation
of anti-symmetrically oriented circles to the symmetric case. By shrinking one
of the circles to zero size we then explicitly work out the first few terms of
the local operator expansion of the loop. Our calculations explicitly
demonstrate that circular Maldacena-Wilson loops are non-BPS observables
precisely due to the appearance of unprotected local operators. The latter
receive anomalous scaling dimensions from non-ladder diagrams. Finally, we
present new insights into a recent conjecture claiming that coincident circular
Maldacena-Wilson loops are described by a Gaussian matrix model. We report on a
novel, supporting two-loop test, but also explain and illustrate why the
existing arguments in favor of the conjecture are flawed.Comment: 16 pages, numerous figure
The Tetrahedron Zamolodchikov Algebra and the AdS5 x S5 S-matrix
The S-matrix of the string theory is a tensor product of
two centrally extended su(2|2) S-matrices, each of which is related to the
R-matrix of the Hubbard model. The R-matrix of the Hubbard model was first
found by Shastry, who ingeniously exploited the fact that, for zero coupling,
the Hubbard model can be decomposed into two XX models. In this article, we
review and clarify this construction from the AdS/CFT perspective and
investigate the implications this has for the S-matrix.Comment: 41 pages, 1 table, revised version, published in Communications in
Mathematical Physics (2017
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