4,013 research outputs found

### A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon

Seven-particle scattering amplitudes in planar super-Yang-Mills theory are
believed to belong to a special class of generalised polylogarithm functions
called heptagon functions. These are functions with physical branch cuts whose
symbols may be written in terms of the 42 cluster A-coordinates on Gr(4,7).
Motivated by the success of the hexagon bootstrap programme for constructing
six-particle amplitudes we initiate the systematic study of the symbols of
heptagon functions. We find that there is exactly one such symbol of weight six
which satisfies the MHV last-entry condition and is finite in the $7 \parallel
6$ collinear limit. This unique symbol is both dihedral and parity-symmetric,
and remarkably its collinear limit is exactly the symbol of the three-loop
six-particle MHV amplitude, although none of these properties were assumed a
priori. It must therefore be the symbol of the three-loop seven-particle MHV
amplitude. The simplicity of its construction suggests that the n-gon bootstrap
may be surprisingly powerful for n>6.Comment: 30 pages, 3 ancillary files, v3: minor corrections, including a typo
in (33

### Tree-Level Amplitudes in N=8 Supergravity

We present an algorithm for writing down explicit formulas for all tree
amplitudes in N=8 supergravity, obtained from solving the supersymmetric
on-shell recursion relations. The formula is patterned after one recently
obtained for all tree amplitudes in N=4 super Yang-Mills which involves nested
sums of dual superconformal invariants. We find that all graviton amplitudes
can be written in terms of exactly the same structure of nested sums with two
modifications: the dual superconformal invariants are promoted from N=4 to N=8
superspace in the simplest manner possible--by squaring them--and certain
additional non-dual conformal gravity dressing factors (independent of the
superspace coordinates) are inserted into the nested sums. To illustrate the
procedure we give explicit closed-form formulas for all NMHV, NNMHV and NNNMV
gravity superamplitudes.Comment: 27 pages, 5 figures, v2: typos correcte

### Explicit Formulas for Neumann Coefficients in the Plane-Wave Geometry

We obtain explicit formulas for the Neumann coefficients and associated
quantities that appear in the three-string vertex for type IIB string theory in
a plane-wave background, for any value of the mass parameter mu. The derivation
involves constructing the inverse of a certain infinite-dimensional matrix, in
terms of which the Neumann coefficients previously had been written only
implicitly. We derive asymptotic expansions for large mu and find unexpectedly
simple results, which are valid to all orders in 1/mu. Using BMN duality, these
give predictions for certain gauge theory quantities to all orders in the
modified 't Hooft coupling lambda'. A specific example is presented.Comment: 28 pages, 2 figures, v2: reference added, new comments and appendix,
typos fixed in eqs. (86) and (89

### Two loop partition function for large N pure Yang-Mills theory on a small three-sphere

We give a direct path-integral calculation of the partition function for pure
3+1 dimensional U(N) Yang-Mills theory at large N on a small three-sphere, up
to two-loop order in perturbation theory. From this, we calculate the one-loop
shift in the Hagedorn/deconfinement temperature for the theory at small volume,
finding that it increases (in units of the inverse sphere radius) as we go to
larger coupling (larger volume). Our results also allow us to read off the sum
of one-loop anomalous dimensions for all operators with a given engineering
dimension in planar Yang-Mills theory on R^4. As checks on our calculation, we
reproduce both the Hagedorn shift and some of the anomalous dimension sums by
independent methods using the results of hep-th/0412029 and hep-th/0408178. The
success of our calculation provides a significant check of methods used in
hep-th/0502149 to establish a first order deconfinement transition for pure
Yang-Mills theory on a small three-sphere.Comment: 40 pages, 4 figures, harvma

### Low Energy Action of "Covariant" Superstring Field Theory in the NS-NS pp-Wave Background

Exact construction of superstring field theory in some background fields is
very important. We construct the low energy NS-NS sector of superstring field
action in the pp-wave background with the flux of NS-NS antisymmetric tensor
field (NS-NS pp-wave) without gauge fixing up to the second-order where the
action is world-sheet BRST invariant. Here we use the word "covariant" in a
invariant theory for a symmetric transformation of the pp-wave background which
is not the Lorentz transformation in the flat background. Moreover we prove the
exact correspondence between this low energy action and the second-order
perturbation of supergravity action in the same background. We also prove the
correspondence of the gauge transformation in both the actions. This
construction is based on the BRST first quantization of superstrings in the
pp-wave background in our previous paper.Comment: 34 page

### Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits

We compute the three-loop contribution to the N=4 supersymmetric Yang-Mills
planar four-gluon amplitude using the recently-proposed Higgs IR regulator of
Alday, Henn, Plefka, and Schuster. In particular, we test the proposed
exponential ansatz for the four-gluon amplitude that is the analog of the BDS
ansatz in dimensional regularization. By evaluating our results at a number of
kinematic points, and also in several kinematic limits, we establish the
validity of this ansatz at the three-loop level.
We also examine the Regge limit of the planar four-gluon amplitude using
several different IR regulators: dimensional regularization, Higgs
regularization, and a cutoff regularization. In the latter two schemes, it is
shown that the leading logarithmic (LL) behavior of the amplitudes, and
therefore the lowest-order approximation to the gluon Regge trajectory, can be
correctly obtained from the ladder approximation of the sum of diagrams. In
dimensional regularization, on the other hand, there is no single dominant set
of diagrams in the LL approximation. We also compute the NLL and NNLL behavior
of the L-loop ladder diagram using Higgs regularization.Comment: 45 pages, 9 figures; v3: major revision (more stringent tests,
discussion of order of limits in the Regge regime

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