25 research outputs found
Edge length dynamics on graphs with applications to -adic AdS/CFT
We formulate a Euclidean theory of edge length dynamics based on a notion of
Ricci curvature on graphs with variable edge lengths. In order to write an
explicit form for the discrete analog of the Einstein-Hilbert action, we
require that the graph should either be a tree or that all its cycles should be
sufficiently long. The infinite regular tree with all edge lengths equal is an
example of a graph with constant negative curvature, providing a connection
with -adic AdS/CFT, where such a tree takes the place of anti-de Sitter
space. We compute simple correlators of the operator holographically dual to
edge length fluctuations. This operator has dimension equal to the dimension of
the boundary, and it has some features in common with the stress tensor.Comment: 42 pages, 6 figure
Melonic theories over diverse number systems
Melonic field theories are defined over the p-adic numbers with the help of a sign character. Our construction works over the reals as well as the p-adics, and it includes the fermionic and bosonic Klebanov-Tarnopolsky models as special cases; depending on the sign character, the symmetry group of the field theory can be either orthogonal or symplectic. Analysis of the Schwinger-Dyson equation for the two-point function in the leading melonic limit shows that power law scaling behavior in the infrared arises for fermionic theories when the sign character is non-trivial, and for bosonic theories when the sign character is trivial. In certain cases, the Schwinger-Dyson equation can be solved exactly using a quartic polynomial equation, and the solution interpolates between the ultraviolet scaling controlled by the spectral parameter and the universal infrared scaling. As a by-product of our analysis, we see that melonic field theories defined over the real numbers can be modified by replacing the time derivative by a bilocal kinetic term with a continuously variable spectral parameter. The infrared scaling of the resulting two-point function is universal, independent of the spectral parameter of the ultraviolet theory
The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps
We present new formulas for -particle tree-level scattering amplitudes of
six-dimensional super Yang-Mills (SYM) and
supergravity (SUGRA). They are written as integrals over
the moduli space of certain rational maps localized on the solutions
of the scattering equations. Due to the properties of spinor-helicity variables
in six dimensions, the even- and odd- formulas are quite different and
have to be treated separately. We first propose a manifestly supersymmetric
expression for the even- amplitudes of SYM theory and
perform various consistency checks. By considering soft-gluon limits of the
even- amplitudes, we deduce the form of the rational maps and the integrand
for odd. The odd- formulas obtained in this way have a new redundancy
that is intertwined with the usual invariance on the
Riemann sphere. We also propose an alternative form of the formulas, analogous
to the Witten-RSV formulation, and explore its relationship with the symplectic
(or Lagrangian) Grassmannian. Since the amplitudes are formulated in a way that
manifests double-copy properties, formulas for the six-dimensional
SUGRA amplitudes follow. These six-dimensional results
allow us to deduce new formulas for five-dimensional SYM and SUGRA amplitudes,
as well as massive amplitudes of four-dimensional SYM on the
Coulomb branch.Comment: 71+23 pages. v2: minor corrections, references added, matches
published JHEP versio
All Tree Amplitudes of 6D (2,0) Supergravity: Interacting Tensor Multiplets and the K3 Moduli Space
We present a twistorlike formula for the complete tree-level
S matrix of six-dimensional (6D) (2,0) supergravity coupled to 21 Abelian tensor multiplets. This is the low-energy effective theory that corresponds to type IIB superstring theory compactified on a K3 surface. The formula is expressed as an integral over the moduli space of certain rational maps of the punctured Riemann sphere. By studying soft limits of the formula, we are able to explore the local moduli space of this theory, {[SO(5,21)]/[SO(5)×SO(21)]. Finally, by dimensional reduction, we also obtain a new formula for the tree-level
S matrix of 4D N=4 Einstein-Maxwell theory.s. C. W. was supported by Royal Society University Research Fellowship No. UF160350. S.-Q. Z. was supported by Royal Society Grant No. RGF\R1\180037. M. H. would like to thank S. S. Gubser and Princeton University for their hospitality, and work done at Princeton was supported in part by the Department of Energy under Grant No. DE-FG02-91ER40671, and by the Simons Foundation, Grant No. 511167 (SSG). M. H. and J. H. S. were supported in part by the Walter Burke Institute for Theoretical Physics at Caltech and by U.S. DOE Grant No. DE-SC001163