arXiv subjects

Luis F. Alday

Publications and source records attributed to Luis F. Alday.

97 records · Page 6Linked to original sources

arXiv2007

Comments on gluon scattering amplitudes via AdS/CFT

In this article we consider n gluon color ordered, planar amplitudes in N=4 super Yang Mills at strong 't Hooft coupling. These amplitudes are approximated by classical surfaces in AdS_5 space. We compute the value of the amplitude for a particular kinematic configuration for a large number of gluons and find that the result disagrees with a recent guess for the exact value of the amplitude. Our results are still compatible with a possible relation between amplitudes and Wilson loops. In addition, we also give a prescription for computing processes involving local operators and asymptotic states with a fixed number of gluons. As a byproduct, we also obtain a string theory prescription for computing the dual of the ordinary Wilson loop, Tr P exp[ i\oint A ], with no couplings to the scalars. We also evaluate the quark-antiquark potential at two loops.

hep-th↗

arXiv2007

Gluon scattering amplitudes at strong coupling

We describe how to compute planar gluon scattering amplitudes at strong coupling in N=4 super Yang Mills by using the gauge/string duality. The computation boils down to finding a certain classical string configuration whose boundary conditions are determined by the gluon momenta. The results are infrared divergent. We introduce the gravity version of dimensional regularization to define finite quantities. The leading and subleading IR divergencies are characterized by two functions of the coupling that we compute at strong coupling. We compute also the full finite form for the four point amplitude and we find agreement with a recent ansatz by Bern, Dixon and Smirnov.

hep-th↗

arXiv2006

The Gravitational Description of Coarse Grained Microstates

In this paper we construct a detailed map from pure and mixed half-BPS states of the D1-D5 system to half-BPS solutions of type IIB supergravity. Using this map, we can see how gravity arises through coarse graining microstates, and we can explicitly confirm the microscopic description of conical defect metrics, the M=0 BTZ black hole and of small black rings. We find that the entropy associated to the natural geometric stretched horizon typically exceeds that of the mixed state from which the geometry was obtained.

hep-th↗

arXiv2006

Towards a string bit formulation of N=4 super Yang-Mills

We show that planar cal N=4 Yang-Mills theory at zero 't Hooft coupling can be efficiently described in terms of 8 bosonic and 8 fermionic oscillators. We show that these oscillators can serve as world-sheet variables, the string bits, of a discretized string. There is a one to one correspondence between the on shell gauge invariant words of the free Y-M theory and the states in the oscillators' Hilbert space, obeying a local gauge and cyclicity constraints. The planar two-point functions and the three-point functions of all gauge invariant words are obtained by the simple delta-function overlap of the corresponding discrete string world sheet. At first order in the 't Hooft coupling, i.e. at one-loop in the Y-M theory, the logarithmic corrections of the planar two-point and the three-point functions can be incorporated by nearest neighbour interactions among the discretized string bits. In the SU(2) sub-sector we show that the one-loop corrections to the structure constants can be uniquely determined by the symmetries of the bit picture. For the SU(2) sub-sector we construct a gauged, linear, discrete world-sheet model for the oscillators, with only nearest neighbour couplings, which reproduces the anomalous dimension Hamiltonian up to two loops. This model also obeys BMN scaling to all loops.

hep-th↗

arXiv2005

What is the dual of a dipole?

We study gravitational solutions that admit a dual CFT description and carry non zero dipole charge. We focus on the black ring solution in AdS_3 x S^3 and extract from it the one-point functions of all CFT operators dual to scalar excitations of the six-dimensional metric. In the case of small black rings, characterized by the level N, angular momentum J and dipole charge q_3, we show how the large N and J dependence of the one-point functions can be reproduced, under certain assumptions, directly from a suitable ensemble in the dual CFT. Finally we present a simple toy model that describes the thermodynamics of the small black ring for arbitrary values of the dipole charge.

hep-th↗

arXiv2005

Structure constants of planar N =4 Yang Mills at one loop

We study structure constants of gauge invariant operators in planar N=4 Yang-Mills at one loop with the motivation of determining features of the string dual of weak coupling Yang-Mills. We derive a simple renormalization group invariant formula characterizing the corrections to structure constants of any primary operator in the planar limit. Applying this to the scalar SO(6) sector we find that the one loop corrections to structure constants of gauge invariant operators is determined by the one loop anomalous dimension Hamiltonian in this sector. We then evaluate the one loop corrections to structure constants for scalars with arbitrary number of derivatives in a given holomorphic direction. We find that the corrections can be characterized by suitable derivatives on the four point tree function of a massless scalar with quartic coupling. We show that individual diagrams violating conformal invariance can be combined together to restore it using a linear inhomogeneous partial differential equation satisfied by this function.

hep-th↗

arXiv2003

Gravitational F-terms through anomaly equations and deformed chiral rings

We study effective gravitational F-terms, obtained by integrating an $U(N)$ adjoint chiral superfield $Φ$ coupled to the ${\cal N}=1$ gauge chiral superfield $W_α$ and supergravity, to arbitrary orders in the gravitational background. The latter includes in addition to the ${\cal N}=1$ Weyl superfield $G_{αβγ}$, the self-dual graviphoton field strength $F_{αβ}$ of the parent, broken ${\cal N}=2$ theory. We first study the chiral ring relations resulting from the above non-standard gravitational background and find agreement, for gauge invariant operators, with those obtained from the dual closed string side via Bianchi identities for ${\cal N}=2$ supergravity coupled to vector multiplets. We then derive generalized anomaly equations for connected correlators on the gauge theory side, which allow us to solve for the basic one-point function $\langle {\rm Tr} W^2/(z-Φ)\rangle$ to all orders in $F^2$. By generalizing the matrix model loop equation to the generating functional of connected correlators of resolvents, we prove that the gauge theory result coincides with the genus expansion of the associated matrix model, after identifying the expansion parameters on the two sides.

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