2,577 research outputs found
Bethe Ansaetze for GKP strings
Studying the scattering of excitations around a dynamical background has a
long history in the context of integrable models. The Gubser-Klebanov-Polyakov
string solution provides such a background for the string/gauge correspondence.
Taking the conjectured all-loop asymptotic equations for the AdS_4/CFT_3
correspondence as the starting point, we derive the S-matrix and a set of
spectral equations for the lowest-lying excitations. We find that these
equations resemble closely the analogous equations for AdS_5/CFT_4, which are
also discussed in this paper. At large values of the coupling constant we show
that they reproduce the Bethe equations proposed to describe the spectrum of
the low-energy limit of the AdS_4xCP^3 sigma model.Comment: 60 pages, 5 figure
Motives: an introductory survey for physicists
We survey certain accessible aspects of Grothendieck's theory of motives in
arithmetic algebraic geometry for mathematical physicists, focussing on areas
that have recently found applications in quantum field theory. An appendix (by
Matilde Marcolli) sketches further connections between motivic theory and
theoretical physics.Comment: LaTeX 35 pages, article by Abhijnan Rej with an appendix by
M.Marcolli. Version II/Final: cosmetic changes to bibliography, added a small
subsection on triangulated categories to section 6. Accepted for publication
in the MPIM-Bonn "Renormalization, combinatorics and physics" proceedings
volum
Supermanifolds from Feynman graphs
We generalize the computation of Feynman integrals of log divergent graphs in
terms of the Kirchhoff polynomial to the case of graphs with both fermionic and
bosonic edges, to which we assign a set of ordinary and Grassmann variables.
This procedure gives a computation of the Feynman integrals in terms of a
period on a supermanifold, for graphs admitting a basis of the first homology
satisfying a condition generalizing the log divergence in this context. The
analog in this setting of the graph hypersurfaces is a graph supermanifold
given by the divisor of zeros and poles of the Berezinian of a matrix
associated to the graph, inside a superprojective space. We introduce a
Grothendieck group for supermanifolds and we identify the subgroup generated by
the graph supermanifolds. This can be seen as a general procedure to construct
interesting classes of supermanifolds with associated periods.Comment: 21 pages, LaTeX, 4 eps figure
Nesting and Dressing
We compute the anomalous dimensions of field strength operators Tr F^L in N=4
SYM from an asymptotic nested Bethe ansatz to all-loop order. Starting from the
exact solution of the one-loop problem at arbitrary L, we derive a single
effective integral equation for the thermodynamic limit of these dimensions. We
also include the recently proposed phase factor for the S-matrix of the planar
AdS/CFT system. The terms in the effective equation corresponding to,
respectively, the nesting and the dressing are structurally very similar. This
hints at the physical origin of the dressing phase, which we conjecture to
arise from the hidden presence of infinitely many auxiliary Bethe roots
describing a non-trivial "filled" structure of the theory's BPS vacuum. We
finally show that the mechanism for creating effective nesting/dressing kernels
is quite generic by also deriving the integral equation for the all-loop
dimension of a certain one-loop so(6) singlet state.Comment: 38 pages, 2 figures. v2: References and appendix discussing the
emulation of the dressing phase adde
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