543 research outputs found
Partition Functions and Casimir Energies in Higher Spin AdS_{d+1}/CFT_d
Recently, the one-loop free energy of higher spin (HS) theories in Euclidean
AdS_{d+1} was calculated and matched with the order N^0 term in the free energy
of the large N "vectorial" scalar CFT on the S^d boundary. Here we extend this
matching to the boundary theory defined on S^1 x S^{d-1}, where the length of
S^1 may be interpreted as the inverse temperature. It has been shown that the
large N limit of the partition function on S^1 x S^2 in the U(N) singlet sector
of the CFT of N free complex scalars matches the one-loop thermal partition
function of the Vasiliev theory in AdS_4, while in the O(N) singlet sector of
the CFT of N real scalars it matches the minimal theory containing even spins
only. We extend this matching to all dimensions d. We also calculate partition
functions for the singlet sectors of free fermion CFT's in various dimensions
and match them with appropriately defined higher spin theories, which for d>3
contain massless gauge fields with mixed symmetry. In the zero-temperature case
R x S^{d-1} we calculate the Casimir energy in the scalar or fermionic CFT and
match it with the one-loop correction in the global AdS_{d+1}. For any
odd-dimensional CFT the Casimir energy must vanish on general grounds, and we
show that the HS duals obey this. In the U(N) symmetric case, we exhibit the
vanishing of the regularized 1-loop Casimir energy of the dual HS theory in
AdS_{d+1}. In the minimal HS theory the vacuum energy vanishes for odd d while
for even d it is equal to the Casimir energy of a single conformal scalar in R
x S^{d-1} which is again consistent with AdS/CFT, provided the minimal HS
coupling constant is ~ 1/(N-1). We demonstrate analogous results for singlet
sectors of theories of N Dirac or Majorana fermions. We also discuss extensions
to CFT's containing N_f flavors in the fundamental representation of U(N) or
O(N).Comment: 43 pages. v3: minor changes, references added. Version published in
PR
"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
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
Wilson loops at large and the quantum M2 brane
The Wilson loop operator in the ABJM theory at
large and fixed level has a dual description in terms of a wrapped M2
brane in the M-theory background AdS. We consider
the localization result for the -BPS circular Wilson loop expectation
value in this regime, and compare it to the prediction of the M2 brane
theory. The leading large exponential factor is matched as expected by the
classical action of the M2 brane solution with AdS geometry. We
show that the subleading -dependent prefactor in is also exactly
reproduced by the one-loop term in the partition function of the wrapped M2
brane (with all Kaluza-Klein modes included). This appears to be the first case
of an exact matching of the overall numerical prefactor in the Wilson loop
expectation value against the dual holographic result. It provides an example
of a consistent quantum M2 brane computation, suggesting various
generalizations.Comment: 13
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.
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
Instanton contributions to the ABJM free energy from quantum M2 branes
We present a quantum M2 brane computation of the instanton prefactor in the
leading non-perturbative contribution to the ABJM 3-sphere free energy at large
and fixed level . Using supersymmetric localization, such instanton
contribution was found earlier to take the form .
The exponent comes from the action of an M2 brane instanton wrapped on
, which represents the M-theory uplift of the
instanton in type IIA string theory on AdS. The IIA string computation of the leading large term in the
instanton prefactor was recently performed in arXiv:2304.12340. Here we find
that the exact value of the prefactor is
reproduced by the 1-loop term in the M2 brane partition function expanded near
the instanton configuration. As in the Wilson loop example
in arXiv:2303.15207, the quantum M2 brane computation is well defined and
produces a finite result in exact agreement with localization.Comment: 27 pages. v2: comments adde
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
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