35 research outputs found
A Feynman integral in Lifshitz-point and Lorentz-violating theories in R<sup>D</sup> âš R<i><sup>m</sup></i>
We evaluate a 1-loop, 2-point, massless Feynman integral ID,m(p,q) relevant for perturbative field theoretic calculations in strongly anisotropic d=D+m dimensional spaces given by the direct sum RD âš Rm . Our results are valid in the whole convergence region of the integral for generic (noninteger) codimensions D and m. We obtain series expansions of ID,m(p,q) in terms of powers of the variable X:=4p2/q4, where p=|p|, q=|q|, p Đ RD, q Đ Rm, and in terms of generalised hypergeometric functions 3F2(âX), when X<1. These are subsequently analytically continued to the complementary region Xâ„1. The asymptotic expansion in inverse powers of X1/2 is derived. The correctness of the results is supported by agreement with previously known special cases and extensive numerical calculations
Lifshitz spacetimes from AdS null and cosmological solutions
We describe solutions of 10-dimensional supergravity comprising null
deformations of with a scalar field, which have
Lifshitz symmetries. The bulk Lifshitz geometry in 3+1-dimensions arises by
dimensional reduction of these solutions. The dual field theory in this case is
a deformation of the N=4 super Yang-Mills theory. We discuss the holographic
2-point function of operators dual to bulk scalars. We further describe
time-dependent (cosmological) solutions which have anisotropic Lifshitz scaling
symmetries. We also discuss deformations of in 11-dimensional
supergravity, which are somewhat similar to the solutions above. In some cases
here, we expect the field theory duals to be deformations of the Chern-Simons
theories on M2-branes stacked at singularities.Comment: Latex, 29pgs, v3. references, minor clarifications (subsection on
Lifshitz geometry seen by scalar probes) added, to appear in JHE
Emergent Lifshitz scaling from N=4 SYM with supersymmetric heavy-quark density
We consider supersymmetric configurations in Type IIB supergravity obtained by the beackreaction of fundamental strings ending on a stack of D3-branes and smeared uniformly in the three spatial directions along the D3-branes. These automatically include a distribution of D5-brane baryon vertices necessary to soak up string charge. The backgrounds are static, preserving eight supersymmetries, an SO(5) global symmetry and symmetry under spatial translations and rotations. We obtain the most general BPS configurations consistent with the symmetries. We show that the solutions to the Type IIB field equations are completely specified by a single function (the dilaton) satisfying a Poisson-like equation in two dimensions. We further find that the equation admits a class of solutions displaying Lifshitz-like scaling with dynamical critical exponent z=7. The equations also admit an asymptotically AdS_5 x S^5 solution deformed by the presence of backreacted string sources that yield a uniform density of heavy quarks in N=4 SYM