473 research outputs found
Hamiltonian study of Supersymmetric Yang-Mills Quantum Mechanics
New results obtained within the recently developed approach to supersymmetric
quantum mechanical systems are presented. The method does not suffer from the
sign problem in any dimensions and is capable to provide any quantum observable
with controllable systematic error. Discussed results include: the spectrum and
Witten index of the D=4 system, and the spectrum of zero volume glueballs in
higher 3 < D < 11 dimensions.Comment: 4 pages, 3 figures, contribution to Lattice200
Heptagon Amplitude in the Multi-Regge Regime
As we have shown in previous work, the high energy limit of scattering
amplitudes in N=4 supersymmetric Yang-Mills theory corresponds to the infrared
limit of the 1-dimensional quantum integrable system that solves minimal area
problems in AdS5. This insight can be developed into a systematic algorithm to
compute the strong coupling limit of amplitudes in the multi-Regge regime
through the solution of auxiliary Bethe Ansatz equations. We apply this
procedure to compute the scattering amplitude for n=7 external gluons in
different multi-Regge regions at infinite 't Hooft coupling. Our formulas are
remarkably consistent with the expected form of 7-gluon Regge cut contributions
in perturbative gauge theory. A full description of the general algorithm and a
derivation of results will be given in a forthcoming paper.Comment: 14 page
Colored Spin Systems, BKP Evolution and finite N_c effects
Even within the framework of the leading logarithmic approximation the
eigenvalues of the BKP kernel for states of more than three reggeized gluons
are unknown in general, contrary to the planar limit case where the problem
becomes integrable. We consider a 4-gluon kernel for a finite number of colors
and define some simple toy models for the configuration space dynamics, which
are directly solvable with group theoretical methods. Then we study the
dependence of the spectrum of these models with respect to the number of colors
and make comparisons with the large limit case.Comment: 17 pages, 4 figures, references update, to appear on EPJ
Quantum systems in a cut Fock space
Standard quantum mechanics is viewed as a limit of a cut system with
artificially restricted dimension of a Hilbert space. Exact spectrum of cut
momentum and coordinate operators is derived and the limiting transition to the
infinite dimensional Hilbert space is studied in detail. The difference between
systems with discrete and continuous energy spectra is emphasized. In
particular a new scaling law, characteristic for nonlocalized, states is found.
Some applications for supersymmetric quantum mechanics are briefly outlined.Comment: 10 page
MHV amplitude for 3->3 gluon scattering in Regge limit
We calculate corrections to the BDS formula for the six-particle planar MHV
amplitude for the gluon transition 3->3 in the multi-Regge kinematics for the
physical region, in which the Regge pole ansatz is not valid. The remainder
function at two loops is obtained by an analytic continuation of the expression
derived by Goncharov, Spradlin, Vergu and Volovich to the kinematic region
described by the Mandelstam singularity exchange in the crossing channel. It
contains both the imaginary and real contributions being in agreement with the
BFKL predictions. The real part of the three loop expression is found from a
dispersion-like all-loop formula for the remainder function in the multi-Regge
kinematics derived by one of the authors. We also make a prediction for the
all-loop real part of the remainder function multiplied by the BDS phase, which
can be accessible through calculations in the regime of the strong coupling
constant.Comment: 6 pages, 4 figure
Semiclassical Strings in AdS_5 x S^5 and Automorphic Functions
Using AdS/CFT we derive from the folded spinning string ordinary differential
equations for the anomalous dimension of the dual N=4 SYM twist-two operators
at strong coupling. We show that for large spin the asymptotic solutions have
the Gribov-Lipatov recirocity property. To obtain this result we use a hidden
modular invariance of the energy-spin relation of the folded spinning string.
Further we identify the Moch-Vermaseren-Vogt (MVV) relations, which were first
recognized in plain QCD calculations, as the recurrence relations of the
asymptotic series ansatz.Comment: 4 page
Integrable spin chains and scattering amplitudes
In this review we show that the multi-particle scattering amplitudes in N=4
SYM at large Nc and in the multi-Regge kinematics for some physical regions
have the high energy behavior appearing from the contribution of the Mandelstam
cuts in the complex angular momentum plane of the corresponding t-channel
partial waves. These Mandelstam cuts or Regge cuts are resulting from gluon
composite states in the adjoint representation of the gauge group SU(Nc). In
the leading logarithmic approximation (LLA) their contribution to the six point
amplitude is in full agreement with the known two-loop result.
The Hamiltonian for the Mandelstam states constructed from n gluons in LLA
coincides with the local Hamiltonian of an integrable open spin chain. We
construct the corresponding wave functions using the integrals of motion and
the Baxter-Sklyanin approach.Comment: Invited review for a special issue of Journal of Physics A devoted to
"Scattering Amplitudes in Gauge Theories", R. Roiban(ed), M. Spradlin(ed), A.
Volovich (ed
Recent progress in supersymmetric Yang-Mills quantum mechanics in various dimensions
We review the last year progress in understanding supersymmetric SU(2)
Yang-Mills quantum mechanics in four and ten space-time dimensions. The four
dimensional system is now well under control and the precise spectrum is
obtained in all channels. In D=10 some new results are also available.Comment: 19 pages, 4 figures, presented at the Workshop on Random Geometry,
Krakow, May 15 - 17, 200
- …