122 research outputs found
The Schur index with Polyakov loops
Recently the Schur index of SYM was evaluated in closed form to
all orders including exponential corrections in the large expansion and for
fixed finite . This was achieved by identifying the matrix model which
calculates the index with the partition function of a system of free fermions
on a circle. The index can be enriched by the inclusion of loop operators and
the case of Wilson loops is particularly easy, as it amounts to inserting extra
characters into the matrix model. The Fermi-gas approach is applied here to
this problem, the formalism is explored and explicit results at large are
found for the fundamental as well as a few other symmetric and antisymmetric
representations.Comment: 15 pages. 1 figur
1/4 BPS circular loops, unstable world-sheet instantons and the matrix model
The standard prescription for computing Wilson loops in the AdS/CFT
correspondence in the large coupling regime and tree-level involves minimizing
the string action. In many cases the action has more than one saddle point as
in the simple example studied in this paper, where there are two 1/4 BPS string
solutions, one a minimum and the other not. Like in the case of the regular
circular loop the perturbative expansion seems to be captured by a free matrix
model. This gives enough analytic control to extrapolate from weak to strong
coupling and find both saddle points in the asymptotic expansion of the matrix
model. The calculation also suggests a new BMN-like limit for nearly BPS Wilson
loop operators.Comment: 13 pages, amste
Wilson Loops as Matrix Strings
In the framework of Matrix theory we show that Wilson loops can serve as
interpolating fields to define string scattering amplitudes as gauge theory
observables.Comment: 5 pages, LaTeX, reference adde
A supermatrix model for N=6 super Chern-Simons-matter theory
We construct the Wilson loop operator of N=6 super Chern-Simons-matter which
is invariant under half of the supercharges of the theory and is dual to the
simplest macroscopic open string in AdS_4 x CP^3. The Wilson loop couples, in
addition to the gauge and scalar fields of the theory, also to the fermions in
the bi-fundamental representation of the U(N) x U(M) gauge group. These
ingredients are naturally combined into a superconnection whose holonomy gives
the Wilson loop, which can be defined for any representation of the supergroup
U(N|M). Explicit expressions for loops supported along an infinite straight
line and along a circle are presented. Using the localization calculation of
Kapustin et al. we show that the circular loop is computed by a supermatrix
model and discuss the connection to pure Chern-Simons theory with supergroup
U(N|M).Comment: 23 page
All-genus calculation of Wilson loops using D-branes
The standard prescription for calculating a Wilson loop in the AdS/CFT
correspondence is by a string world-sheet ending along the loop at the boundary
of AdS. For a multiply wrapped Wilson loop this leads to many coincident
strings, which may interact among themselves. In such cases a better
description of the system is in terms of a D3-brane carrying electric flux. We
find such solutions for the single straight line and the circular loop. The
action agrees with the string calculation at small coupling and in addition
captures all the higher genus corrections at leading order in alpha'. The
resulting expression is in remarkable agreement with that found from a zero
dimensional Gaussian matrix model.Comment: 29 pages, LeTeX, one colour figure. v2: citation corrected. v3: minor
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3d mirror symmetry as a canonical transformation
We generalize the free Fermi-gas formulation of certain 3d
supersymmetric Chern-Simons-matter theories by allowing Fayet-Iliopoulos
couplings as well as mass terms for bifundamental matter fields. The resulting
partition functions are given by simple modifications of the argument of the
Airy function found previously. With these extra parameters it is easy to see
that mirror-symmetry corresponds to linear canonical transformations on the
phase space (or operator algebra) of the 1-dimensional fermions.Comment: 11 pages, 2 figures. v2: figure added - version published in JHE
Circular loop operators in conformal field theories
We use the conformal group to study non-local operators in conformal field
theories. A plane or a sphere (of any dimension) is mapped to itself by some
subgroup of the conformal group, hence operators confined to that submanifold
may be classified in representations of this subgroup. For local operators this
gives the usual definition of conformal dimension and spin, but some conformal
field theories contain interesting nonlocal operators, like Wilson or 't Hooft
loops. We apply those ideas to Wilson loops in four-dimensional CFTs and show
how they can be chosen to be in fixed representations of SL(2,R) x SO(3).Comment: 10 pages, late
Generalized quark-antiquark potential in AdS/CFT
In this talk we present a family of Wilson loop operators which continuously
interpolates between the 1/2 BPS line and the antiparallel lines, and can be
thought of as calculating a generalization of the quark--antiquark potential
for the gauge theory on S^3 x R. We evaluate the first two orders of these
loops perturbatively both in the gauge and string theory. We obtain analytical
expressions in a systematic expansion around the 1/2 BPS configuration, and
comment on possible all-loop patterns for these Wilson loops.Comment: 6 pages. Proceedings of the "XVII European Workshop on String Theory
2011", Padova, Italy, 5-9 September 201
An exact prediction of [script N] = 4 supersymmetric Yang–Mills theory for string theory
We propose that the expectation value of a circular BPS-Wilson loop in [script N] = 4 supersymmetric Yang–Mills can be calculated exactly, to all orders in a 1/N expansion and to all orders in g2N. 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[prime] and to all orders in gs. We then compare this result with string theory. We find that the gauge theory calculation, for large g2N and to all orders in the 1/N2 expansion, does agree with the leading string theory calculation, to all orders in gs and to lowest order in alpha[prime]. 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
Cutting and Sewing Riemann Surfaces in Mathematics, Physics and Clay
A series of ceramic artworks are presented, inspired by the author's research
connecting theoretical physics to the beautiful theory of Riemann surfaces.
More specifically the research is related to the classification of curves on
the surfaces based on a description of them as built from basic building blocks
known as "pairs of pants". The relevant background on this mathematics of these
two dimensional spaces is outlined, some of the artistic process is explained:
Both the conceptual ideas and their implementation. Many photos of the ceramics
are included to illustrate this and the connected physics problem is briefly
mentioned.Comment: Work presented at the Bridges Math-Art conference, Aalto University,
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