1,026 research outputs found
An Exact Prediction of N=4 SUSYM Theory for String Theory
We propose that the expectation value of a circular BPS-Wilson loop in N=4
SUSYM can be calculated exactly, to all orders in a 1/N expansion and to all
orders in g^2 N. Using the AdS/CFT duality, this result yields a prediction of
the value of the string amplitude with a circular boundary to all orders in
alpha' and to all orders in g_s. We then compare this result with string
theory. We find that the gauge theory calculation, for large g^2 N and to all
orders in the 1/N^2 expansion does agree with the leading string theory
calculation, to all orders in g_s and to lowest order in alpha'. We also find a
relation between the expectation value of any closed smooth Wilson loop and the
loop related to it by an inversion that takes a point along the loop to
infinity, and compare this result, again successfully, with string theory.Comment: LaTeX, 22 pages, 3 figures. Argument corrected and two new sections
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An exact formula for the radiation of a moving quark in N=4 super Yang Mills
We derive an exact formula for the cusp anomalous dimension at small angles.
This is done by relating the latter to the computation of certain 1/8 BPS
Wilson loops which was performed by supersymmetric localization. This function
of the coupling also determines the power emitted by a moving quark in N=4
super Yang Mills, as well as the coefficient of the two point function of the
displacement operator on the Wilson loop. By a similar method we compute the
near BPS expansion of the generalized cusp anomalous dimension.Comment: 22 pages, 5 figures. v2: references added, typos correcte
Analytic Solution of Bremsstrahlung TBA
We consider the quark--anti-quark potential on the three sphere or the
generalized cusp anomalous dimension in planar N=4 SYM. We concentrate on the
vacuum potential in the near BPS limit with units of R-charge.
Equivalently, we study the anomalous dimension of a super-Wilson loop with L
local fields inserted at a cusp. The system is described by a recently proposed
infinite set of non-linear integral equations of the Thermodynamic Bethe Ansatz
(TBA) type. That system of TBA equations is very similar to the one of the
spectral problem but simplifies a bit in the near BPS limit. Using techniques
based on the Y-system of functional equations we first reduced the infinite
system of TBA equations to a Finite set of Nonlinear Integral Equations
(FiNLIE). Then we solve the FiNLIE system analytically, obtaining a simple
analytic result for the potential! Surprisingly, we find that the system has
equivalent descriptions in terms of an effective Baxter equation and in terms
of a matrix model. At L=0, our result matches the one obtained before using
localization techniques. At all other L's, the result is new. Having a new
parameter, L, allows us to take the large L classical limit. We use the matrix
model description to solve the classical limit and match the result with a
string theory computation. Moreover, we find that the classical string
algebraic curve matches the algebraic curve arising from the matrix model.Comment: 50 pages, 5 figures. v2: references added, JHEP versio
Impure Aspects of Supersymmetric Wilson Loops
We study a general class of supersymmetric Wilson loops operator in N = 4
super Yang-Mills theory, obtained as orbits of conformal transformations. These
loops are the natural generalization of the familiar circular Wilson-Maldacena
operator and their supersymmetric properties are encoded into a Killing spinor
that is not pure. We present a systematic analysis of their scalar couplings
and of the preserved supercharges, modulo the action of the global symmetry
group, both in the compact and in the non-compact case. The quantum behavior of
their expectation value is also addressed, in the simplest case of the
Lissajous contours: explicit computations at weak-coupling, through Feynman
diagrams expansion, and at strong-coupling, by means of AdS/CFT correspondence,
suggest the possibility of an exact evaluation.Comment: 40 pages, 4 figure
Ladders for Wilson Loops Beyond Leading Order
We set up a general scheme to resum ladder diagrams for the quark-anti-quark
potential in N=4 super-Yang-Mills theory, and do explicit calculations at the
next-to-leading order. The results perfectly agree with string theory in
AdS(5)xS(5) when continued to strong coupling, in spite of a potential
order-of-limits problem.Comment: 18 pages, 5 figure
Surface Operators in N=2 4d Gauge Theories
N=2 four dimensional gauge theories admit interesting half BPS surface
operators preserving a (2,2) two dimensional SUSY algebra. Typical examples are
(2,2) 2d sigma models with a flavor symmetry which is coupled to the 4d gauge
fields. Interesting features of such 2d sigma models, such as (twisted) chiral
rings, and the tt* geometry, can be carried over to the surface operators, and
are affected in surprising ways by the coupling to 4d degrees of freedom. We
will describe in detail a relation between the parameter space of twisted
couplings of the surface operator and the Seiberg-Witten geometry of the bulk
theory. We will discuss a similar result about the tt* geometry of the surface
operator. We will predict the existence and general features of a wall-crossing
formula for BPS particles bound to the surface operator.Comment: 25 pages, 4 figure
Holography of Wilson-Loop Expectation Values with Local Operator Insertions
We study the expectation values of Wilson-loop operators with the
insertionsof local operators Z^J and Zbar^J with large R-charge J from the bulk
viewpoint of AdS/CFT correspondence. Classical solutions of strings attached to
such deformed Wilson loops at the conformal boundary are constructed and are
applied to the computation of Wilson-loop expectation values. We argue that in
order to have such solutions for general insertions at finite positions in the
base spacetime of the gauge theory, it is crucial to interpret the holographic
correspondence in the semi-classical picture as a tunneling phenomenon, as has
been previously established for holographic computations of correlators of BMN
operators. This also requires to use the Euclideanized AdS background and
Euclidean super Yang-Mills theory.Comment: 16 pages, 5 figures, version to be published in JHEP, no change from
the previous version, only extraneous figure file is remove
Open string fluctuations in AdS_5xS^5 and operators with large R-charge
A semiclassical string description is given for correlators of Wilson loops
with local operators in N=4 SYM theory in the regime when operators carry
parametrically large R-charge. The OPE coefficients of the circular Wilson loop
in chiral primary operators are computed to all orders in the alpha' expansion
in AdS_5xS^5 string theory. The results agree with field-theory predictions.Comment: 16 pages, 2 figures; v2: five misprints correcte
Correlators of supersymmetric Wilson-loops, protected operators and matrix models in N=4 SYM
We study the correlators of a recently discovered family of BPS Wilson loops
in supersymmetric U(N) Yang-Mills theory. When the contours lie on
a two-sphere in the space-time, we propose a closed expression that is valid
for all values of the coupling constant and for any rank , by exploiting
the suspected relation with two-dimensional gauge theories. We check this
formula perturbatively at order for two latitude Wilson loops
and we show that, in the limit where one of the loops shrinks to a point,
logarithmic corrections in the shrinking radius are absent at .
This last result strongly supports the validity of our general expression and
suggests the existence of a peculiar protected local operator arising in the
OPE of the Wilson loop. At strong coupling we compare our result to the string
dual of the SYM correlator in the limit of large separation,
presenting some preliminary evidence for the agreement.Comment: 20 page, 8 figure
Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS
We study correlation functions of Wilson loops and local operators in a
subsector of N=4 SYM which preserves two supercharges. Localization arguments
allow to map the problem to a calculation in bosonic two-dimensional Yang-Mills
theory. In turn, this can be reduced to computing correlators in certain
Gaussian multi-matrix models. We focus on the correlation function of a Wilson
loop and two local operators, and solve the corresponding three-matrix model
exactly in the planar limit. We compare the strong coupling behavior to string
theory in AdS_5xS^5, finding precise agreement. We pay particular attention to
the case in which the local operators have large R-charge J \sim sqrt{lambda}
at strong coupling.Comment: 50 pages, 9 figures. v2: minor changes, references adde
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