113 research outputs found
More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
We perform exact computations of correlation functions of 1/2-BPS local
operators and protected operator insertions on the 1/8-BPS Wilson loop in
SYM. This generalizes the results of our previous paper
arXiv:1802.05201, which employs supersymmetric localization, OPE and the
Gram-Schmidt process. In particular, we conduct a detailed analysis for the
1/2-BPS circular (or straight) Wilson loop in the planar limit, which defines
an interesting nontrivial defect CFT. We compute its bulk-defect structure
constants at finite 't Hooft coupling, and present simple integral expressions
in terms of the -functions that appear in the Quantum Spectral Curve---a
formalism originally introduced for the computation of the operator spectrum.
The results at strong coupling are found to be in precise agreement with the
holographic calculation based on perturbation theory around the AdS string
worldsheet, where they correspond to correlation functions of open string
fluctuations and closed string vertex operators inserted on the worldsheet.
Along the way, we clarify several aspects of the Gram-Schmidt analysis which
were not addressed in the previous paper. In particular, we clarify the role
played by the multi-trace operators at the non-planar level, and confirm its
importance by computing the non-planar correction to the defect two-point
function. We also provide a formula for the first non-planar correction to the
defect correlators in terms of the Quantum Spectral Curve, which suggests the
potential applicability of the formalism to the non-planar correlation
functions.Comment: 44 pages + appendices. v2 references adde
Double-Trace Flows and the Swampland
We explore the idea that large , non-supersymmetric conformal field
theories with a parametrically large gap to higher spin single-trace operators
may be obtained as infrared fixed points of relevant double-trace deformations
of superconformal field theories. After recalling the AdS interpretation and
some potential pathologies of such flows, we introduce a concrete example that
appears to avoid them: the ABJM theory at finite , deformed by , where is the superconformal primary in the stress-tensor
multiplet. We address its relation to recent conjectures based on weak gravity
bounds, and discuss the prospects for a wider class of similarly viable flows.
Next, we proceed to analyze the spectrum and correlation functions of the
putative IR CFT, to leading non-trivial order in . This includes analytic
computations of the change under double-trace flow of connected four-point
functions of ABJM superconformal primaries; and of the IR anomalous dimensions
of infinite classes of double-trace composite operators. These would be the
first analytic results for anomalous dimensions of finite-spin composite
operators in any large CFT with an Einstein gravity dual.Comment: 25+13 pages. v2: refs added, minor clarification
Interpolating between and
We study the dimensional continuation of the sphere free energy in conformal
field theories. In continuous dimension we define the quantity , where is the path integral of the Euclidean CFT on
the -dimensional round sphere. smoothly interpolates between
times the -anomaly coefficient in even , and
times the sphere free energy in odd . We calculate
in various examples of unitary CFT that can be continued to
non-integer dimensions, including free theories, double-trace deformations at
large , and perturbative fixed points in the expansion. For all
these examples is positive, and it decreases under RG flow. Using
perturbation theory in the coupling, we calculate in the
Wilson-Fisher fixed point of the vector model in to order
. We use this result to estimate the value of in the
3-dimensional Ising model, and find that it is only a few percent below of
the free conformally coupled scalar field. We use similar methods to estimate
the values for the Gross-Neveu model in and the model
in . Finally, we carry out the dimensional continuation of interacting
theories with 4 supercharges, for which we suggest that may be
calculated exactly using an appropriate version of localization on . Our
approach provides an interpolation between the -maximization in and
the -maximization in .Comment: 41 pages, 4 figures. v4: Eqs. (1.6), (4.13) and (5.37) corrected;
footnote 9 added discussing the Euler density counterter
One Loop Tests of Higher Spin AdS/CFT
Vasiliev's type A higher spin theories in AdS4 have been conjectured to be
dual to the U(N) or O(N) singlet sectors in 3-d conformal field theories with
N-component scalar fields. We compare the O(N^0) correction to the 3-sphere
free energy F in the CFTs with corresponding calculations in the higher spin
theories. This requires evaluating a regularized sum over one loop vacuum
energies of an infinite set of massless higher spin gauge fields in Euclidean
AdS4. For the Vasiliev theory including fields of all integer spin and a scalar
with Delta=1 boundary condition, we show that the regularized sum vanishes.
This is in perfect agreement with the vanishing of subleading corrections to F
in the U(N) singlet sector of the theory of N free complex scalar fields. For
the minimal Vasiliev theory including fields of only even spin, the regularized
sum remarkably equals the value of F for one free real scalar field. This
result may agree with the O(N) singlet sector of the theory of N real scalar
fields, provided the coupling constant in the Vasiliev theory is identified as
G_N ~ 1/(N-1). Similarly, consideration of the USp(N) singlet sector for N
complex scalar fields, which we conjecture to be dual to the husp(2;0|4)
Vasiliev theory, requires G_N ~ 1/(N+1). We also test the higher spin AdS3/CFT2
conjectures by calculating the regularized sum over one loop vacuum energies of
higher spin fields in AdS3. We match the result with the O(N^0) term in the
central charge of the W_N minimal models; this requires a certain truncation of
the CFT operator spectrum so that the bulk theory contains two real scalar
fields with the same boundary conditions.Comment: 20 pages. v3: minor corrections, version published in JHE
One-loop Partition Functions of 3D Gravity
We consider the one-loop partition function of free quantum field theory in
locally Anti-de Sitter space-times. In three dimensions, the one loop
determinants for scalar, gauge and graviton excitations are computed explicitly
using heat kernel techniques. We obtain precisely the result anticipated by
Brown and Henneaux: the partition function includes a sum over "boundary
excitations" of AdS3, which are the Virasoro descendants of empty Anti-de
Sitter space. This result also allows us to compute the one-loop corrections to
the Euclidean action of the BTZ black hole as well its higher genus
generalizations.Comment: 28 page
Spinning AdS Loop Diagrams: Two Point Functions
We develop a systematic approach to evaluating AdS loop amplitudes based on
the spectral (or "split") representation of bulk-to-bulk propagators, which
re-expresses loop diagrams in terms of spectral integrals and higher-point tree
diagrams. In this work we focus on 2pt one-loop Witten diagrams involving
totally symmetric fields of arbitrary mass and integer spin. As an application
of this framework, we study the contribution to the anomalous dimension of
higher-spin currents generated by bubble diagrams in higher-spin gauge theories
on AdS.Comment: 54+23 pages, 15 figures. v2: Section 2.2 added with more details on
the analytic evaluation of anomalous dimensions from bubble diagrams.
References added, matches published versio
Non-supersymmetric Wilson loop in N=4 SYM and defect 1d CFT
Following Polchinski and Sully (arXiv:1104.5077), we consider a generalized
Wilson loop operator containing a constant parameter in front of the
scalar coupling term, so that corresponds to the standard Wilson
loop, while to the locally supersymmetric one. We compute the
expectation value of this operator for circular loop as a function of
to second order in the planar weak coupling expansion in N=4 SYM theory. We
then explain the relation of the expansion near the two conformal points
and to the correlators of scalar operators inserted on the
loop. We also discuss the string 1-loop correction to the
strong-coupling expansion of the standard circular Wilson loop, as well as its
generalization to the case of mixed boundary conditions on the five-sphere
coordinates, corresponding to general . From the point of view of the
defect 1d CFT defined on the Wilson line, the -dependent term can be
seen as a perturbation driving a RG flow from the standard Wilson loop in the
UV to the supersymmetric Wilson loop in the IR. Both at weak and strong
coupling we find that the logarithm of the expectation value of the standard
Wilson loop for the circular contour is larger than that of the supersymmetric
one, which appears to be in agreement with the 1d analog of the F-theorem.Comment: 36 pages, 3 figures. v3: minor corrections and references adde
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