596 research outputs found
On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
Chern-Simons gauge theories coupled to massless fundamental scalars or
fermions define interesting non-supersymmetric 3d CFTs that possess approximate
higher-spin symmetries at large N. In this paper, we compute the scaling
dimensions of the higher-spin operators in these models, to leading order in
the 1/N expansion and exactly in the 't Hooft coupling. We obtain these results
in two independent ways: by using conformal symmetry and the classical
equations of motion to fix the structure of the current non-conservation, and
by a direct Feynman diagram calculation. The full dependence on the 't Hooft
coupling can be restored by using results that follow from the weakly broken
higher-spin symmetry. This analysis also allows us to obtain some explicit
results for the non-conserved, parity-breaking structures that appear in planar
three-point functions of the higher-spin operators. At large spin, we find that
the anomalous dimensions grow logarithmically with the spin, in agreement with
general expectations. This logarithmic behavior disappears in the strong
coupling limit, where the anomalous dimensions turn into those of the critical
O(N) or Gross-Neveu models, in agreement with the conjectured 3d bosonization
duality.Comment: 52 pages, 7 figures. v3: Minor correction
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
Quantum dispersion relations for excitations of long folded spinning superstring in AdS_5 x S^5
We use AdS_5 x S^5 superstring sigma model perturbation theory to compute the
leading one-loop corrections to the dispersion relations of the excitations
near a long spinning string in AdS. This investigation is partially motivated
by the OPE-based approach to the computation of the expectation value of null
polygonal Wilson loops suggested in arXiv:1006.2788. Our results are in partial
agreement with the recent asymptotic Bethe ansatz computation in
arXiv:1010.5237. In particular, we find that the heaviest AdS mode (absent in
the ABA approach) is stable and has a corrected one-loop dispersion relation
similar to the other massive modes. Its stability might hold also at the
next-to-leading order as we suggest using a unitarity-based argument.Comment: 22 pages, 3 figures. v3: small corrections and a comment added in
sec. 4.
"Short" spinning strings and structure of quantum AdS_5 x S^5 spectrum
Using information from the marginality conditions of vertex operators for the
AdS_5 x S^5 superstring, we determine the structure of the dependence of the
energy of quantum string states on their conserved charges and the string
tension proportional to lambda^(1/2). We consider states on the leading Regge
trajectory in the flat space limit which carry one or two (equal) spins in
AdS_5 or S^5 and an orbital momentum in S^5, with Konishi multiplet states
being particular cases. We argue that the coefficients in the energy may be
found by using a semiclassical expansion. By analyzing the examples of folded
spinning strings in AdS_5 and S^5 as well as three cases of circular two-spin
strings we demonstrate the universality of transcendental (zeta-function) parts
of few leading coefficients. We also show the consistency with target space
supersymmetry with different states belonging to the same multiplet having the
same non-trivial part of the energy. We suggest, in particular, that a rational
coefficient (found by Basso for the folded string using Bethe Ansatz
considerations and which, in general, is yet to be determined by a direct
two-loop string calculation) should, in fact, be universal.Comment: 42p, Latex v2: Comments and summary table of coefficients added v3:
misprints corrected; dependence on winding number added in appendix
Wilson loop in general representation and RG flow in 1d defect QFT
The generalized Wilson loop operator interpolating between the supersymmetric and the ordinary Wilson loop in N=4 SYM theory provides an interesting example of renormalization group flow on a line defect: the scalar coupling parameter ζ has a non-trivial beta function and may be viewed as a running coupling constant in a 1d defect QFT. In this paper we continue the study of this operator, generalizing previous results for the beta function and Wilson loop expectation value to the case of an arbitrary representation of the gauge group and beyond the planar limit. Focusing on the scalar ladder limit where the generalized Wilson loop reduces to a purely scalar line operator in a free adjoint theory, and specializing to the case of the rank k symmetric representation of SU(N), we also consider a certain semiclassical limit where k is taken to infinity with the product kζ2 fixed. This limit can be conveniently studied using a 1d defect QFT representation in terms of N commuting bosons. Using this representation, we compute the beta function and the circular loop expectation value in the large k limit, and use it to derive constraints on the structure of the beta function for general representation. We discuss the corresponding 1d RG flow and comment on the consistency of the results with the 1d defect version of the F-theorem
AdS Description of Induced Higher-Spin Gauge Theory
We study deformations of three-dimensional large N CFTs by double-trace
operators constructed from spin s single-trace operators of dimension \Delta.
These theories possess UV fixed points, and we calculate the change of the
3-sphere free energy \delta F= F_{UV}- F_{IR}. To describe the UV fixed point
using the dual AdS_4 space we modify the boundary conditions on the spin s
field in the bulk; this approach produces \delta F in agreement with the field
theory calculations. If the spin s operator is a conserved current, then the
fixed point is described by an induced parity invariant conformal spin s gauge
theory. The low spin examples are QED_3 (s=1) and the 3-d induced conformal
gravity (s=2). When the original CFT is that of N conformal complex scalar or
fermion fields, the U(N) singlet sector of the induced 3-d gauge theory is dual
to Vasiliev's theory in AdS_4 with alternate boundary conditions on the spin s
massless gauge field. We test this correspondence by calculating the leading
term in \delta F for large N. We show that the coefficient of (1/2)\log N in
\delta F is equal to the number of spin s-1 gauge parameters that act trivially
on the spin s gauge field. We discuss generalizations of these results to 3-d
gauge theories including Chern-Simons terms and to theories where s is
half-integer. We also argue that the Weyl anomaly a-coefficients of conformal
spin s theories in even dimensions d, such as that of the Weyl-squared gravity
in d=4, can be efficiently calculated using massless spin s fields in AdS_{d+1}
with alternate boundary conditions. Using this method we derive a simple
formula for the Weyl anomaly a-coefficients of the d=4 Fradkin-Tseytlin
conformal higher-spin gauge fields. Similarly, using alternate boundary
conditions in AdS_3 we reproduce the well-known central charge c=-26 of the bc
ghosts in 2-d gravity, as well as its higher-spin generalizations.Comment: 62 pages, 1 figure; v2 refs added, minor improvements; v3 refs added,
minor improvement
Constraining conformal field theories with a slightly broken higher spin symmetry
We consider three dimensional conformal field theories that have a higher
spin symmetry that is slightly broken. The theories have a large N limit, in
the sense that the operators separate into single trace and multitrace and obey
the usual large N factorization properties. We assume that the spectrum of
single trace operators is similar to the one that one gets in the Vasiliev
theories. Namely, the only single trace operators are the higher spin currents
plus an additional scalar. The anomalous dimensions of the higher spin currents
are of order 1/N. Using the slightly broken higher spin symmetry we constrain
the three point functions of the theories to leading order in N. We show that
there are two families of solutions. One family can be realized as a theory of
N fermions with an O(N) Chern-Simons gauge field, the other as a N bosons plus
the Chern-Simons gauge field. The family of solutions is parametrized by the 't
Hooft coupling. At special parity preserving points we get the critical O(N)
models, both the Wilson-Fisher one and the Gross-Neveu one. Our analysis also
fixes the on shell three point functions of Vasiliev's theory on AdS_4 or dS_4.Comment: 54 pages, 3 figure
Supersymmetric Chern-Simons Theories with Vector Matter
In this paper we discuss SU(N) Chern-Simons theories at level k with both
fermionic and bosonic vector matter. In particular we present an exact
calculation of the free energy of the N=2 supersymmetric model (with one chiral
field) for all values of the 't Hooft coupling in the large N limit. This is
done by using a generalization of the standard Hubbard-Stratanovich method
because the SUSY model contains higher order polynomial interactions.Comment: 46 pages, 24 figures, v2: comments and references added, v3: a
footnote in Section 3.5 adde
Accidental Symmetries and the Conformal Bootstrap
We study an supersymmetric generalization of the
three-dimensional critical vector model that is described by
chiral superfields with superpotential . By
combining the tools of the conformal bootstrap with results obtained through
supersymmetric localization, we argue that this model exhibits a symmetry
enhancement at the infrared superconformal fixed point due to flowing to
zero. This example is special in that the existence of an infrared fixed point
with , which does not exhibit symmetry enhancement, does not
generally lead to any obvious unitarity violations or other inconsistencies. We
do show, however, that the -theorem excludes the models with
for . The conformal bootstrap provides a stronger constraint and excludes
such models for . We provide evidence that the models, which have
the enhanced symmetry, come close to saturating the bootstrap
bounds. We extend our analysis to fractional dimensions where we can motivate
the nonexistence of the models by studying them perturbatively
in the expansion.Comment: 26 pages, 5 figure
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