1,779 research outputs found
Some analytic results for two-loop scattering amplitudes
We present analytic results for the finite diagrams contributing to the
two-loop eight-point MHV scattering amplitude of planar N=4 SYM. We use a
recently proposed representation for the integrand of the amplitude in terms of
(momentum) twistors and focus on a restricted kinematics in which the answer
depends only on two independent cross-ratios. The theory of motives can be used
to vastly simplify the results, which can be expressed as simple combinations
of classical polylogarithms.Comment: 18 page
Some properties of the Alday-Maldacena minimum
The Alday-Maldacena solution, relevant to the n=4 gluon amplitude in N=4 SYM
at strong coupling, was recently identified as a minimum of the regularized
action in the moduli space of solutions of the AdS_5 sigma-model equations of
motion. Analogous solutions of the Nambu-Goto equations for the n=4 case are
presented and shown to form (modulo the reparametrization group) an equally
large but different moduli space, with the Alday-Maldacena solution at the
intersection of the sigma-model and Nambu-Goto moduli spaces. We comment upon
the possible form of the regularized action for n=5. A function of moduli
parameters z_a is written, whose minimum reproduces the BDDK one-loop
five-gluon amplitude. This function may thus be considered as some kind of
Legendre transform of the BDDK formula and has its own value independently of
the Alday-Maldacena approach.Comment: 10 page
A note on string solutions in AdS_3
We systematically search for classical open string solutions in AdS_3 within
the general class expressed by elliptic functions (i.e., the genus-one
finite-gap solutions). By explicitly solving the reality and Virasoro
conditions, we give a classification of the allowed solutions. When the
elliptic modulus degenerates, we find a class of solutions with six null
boundaries, among which two pairs are collinear. By adding the S^1 sector, we
also find four-cusp solutions with null boundaries expressed by the elliptic
functions.Comment: 17 pages, 1 figure; (v2) added 1 figure and discussion on solutions
with 6 null boundaries; (v3) corrected equation numbers; (v4) added comment
Liouville/Toda central charges from M5-branes
We show that the central charge of the Liouville and ADE Toda theories can be
reproduced by equivariantly integrating the anomaly eight-form of the
corresponding six-dimensional N=(0,2) theories, which describe the low-energy
dynamics of M5-branes.Comment: 9 page
Note About Integrability and Gauge Fixing for Bosonic String on AdS(5)xS(5)
This short note is devoted to the study of the integrability of the bosonic
string on AdS(5)xS(5) in the uniform light-cone gauge. We construct Lax
connection for gauge fixed theory and we argue that it is flat.Comment: 17 page
Vías de intercambio y promoción del campaniforme marítimo y mixto sobre el interior peninsular
El trabajo recoge exhaustivamente información sobre los campaniformes
internacionales de la Península Ibérica (puntillados y mixtos). Observando su ubicación se propone
una vía de distribución terrestre en vez de marítima. Por último se avisa sobre el hecho de que a
medida que los items campaniformes se van integrando entre los grupos aparecerán en contextos
variados: funerarios y de habitación (en un segundo momento)
A finite analog of the AGT relation I: finite W-algebras and quasimaps' spaces
Recently Alday, Gaiotto and Tachikawa proposed a conjecture relating
4-dimensional super-symmetric gauge theory for a gauge group G with certain
2-dimensional conformal field theory. This conjecture implies the existence of
certain structures on the (equivariant) intersection cohomology of the
Uhlenbeck partial compactification of the moduli space of framed G-bundles on
P^2. More precisely, it predicts the existence of an action of the
corresponding W-algebra on the above cohomology, satisfying certain properties.
We propose a "finite analog" of the (above corollary of the) AGT conjecture.
Namely, we replace the Uhlenbeck space with the space of based quasi-maps from
P^1 to any partial flag variety G/P of G and conjecture that its equivariant
intersection cohomology carries an action of the finite W-algebra U(g,e)
associated with the principal nilpotent element in the Lie algebra of the Levi
subgroup of P; this action is expected to satisfy some list of natural
properties. This conjecture generalizes the main result of arXiv:math/0401409
when P is the Borel subgroup. We prove our conjecture for G=GL(N), using the
works of Brundan and Kleshchev interpreting the algebra U(g,e) in terms of
certain shifted Yangians.Comment: minor change
Correlation functions, null polygonal Wilson loops, and local operators
We consider the ratio of the correlation function of n+1 local operators over
the correlator of the first n of these operators in planar N=4 super-Yang-Mills
theory, and consider the limit where the first n operators become pairwise null
separated. By studying the problem in twistor space, we prove that this is
equivalent to the correlator of a n-cusp null polygonal Wilson loop with the
remaining operator in general position, normalized by the expectation value of
the Wilson loop itself, as recently conjectured by Alday, Buchbinder and
Tseytlin. Twistor methods also provide a BCFW-like recursion relation for such
correlators. Finally, we study the natural extension where n operators become
pairwise null separated with k operators in general position. As an example, we
perform an analysis of the resulting correlator for k=2 and discuss some of the
difficulties associated to fixing the correlator completely in the strong
coupling regime.Comment: 34 pages, 6 figures. v2: typos corrected and references added; v3:
published versio
Some comments on spacelike minimal surfaces with null polygonal boundaries in
We discuss some geometrical issues related to spacelike minimal surfaces in
with null polygonal boundaries at conformal infinity. In particular for
, two holomorphic input functions for the Pohlmeyer reduced system are
identified. This system contains two coupled differential equations for two
functions and , related to curvature and
torsion of the surface. Furthermore, we conjecture that, for a polynomial
choice of the two holomorphic functions, the relative positions of their zeros
encode the conformal invariant data of the boundary null -gon.Comment: 13 pages, a note and references added, version to appear in JHE
AGT on the S-duality Wall
Three-dimensional gauge theory T[G] arises on a domain wall between
four-dimensional N=4 SYM theories with the gauge groups G and its S-dual G^L.
We argue that the N=2^* mass deformation of the bulk theory induces a
mass-deformation of the theory T[G] on the wall. The partition functions of the
theory T[SU(2)] and its mass-deformation on the three-sphere are shown to
coincide with the transformation coefficient of Liouville one-point conformal
block on torus under the S-duality.Comment: 14 pages, 3 figures. v2: Revised the analysis in sections 3.3 and 4.
Notes and references added. Version to appear in JHE
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