459 research outputs found
Bounds on Operator Dimensions in 2D Conformal Field Theories
We extend the work of Hellerman (arxiv:0902.2790) to derive an upper bound on
the conformal dimension of the next-to-lowest nontrival primary
operator in unitary two-dimensional conformal field theories without chiral
primary operators. The bound we find is of the same form as found for
: . We find a similar bound on the
conformal dimension , and present a method for deriving bounds on
for any , under slightly modified assumptions. For asymptotically
large and fixed , we show that . We conclude with a brief discussion of the
gravitational implications of these results.Comment: Corrected typos; revised arguments (adding detail) for clarity,
results unchange
A counterexample to the a-'theorem'
The conclusion of the original paper was wrong, due to the incorrect
assumption that the low-energy limit at the strongly-coupled point consists of
a single, coupled SCFT. By taking into account the fact that the low-energy
limit consists of multiple decoupled parts, it was later shown in
arXiv:1011.4568 that there is no violation of the a-theorem in this system.
Furthermore, the a-theorem itself was convincingly demonstrated in
arXiv:1107.3987, and the argument presented there has been further refined. The
rest of this paper is kept as it was, for some parts of the discussions might
still be of interest.
Original abstract: We exhibit a renormalization group flow for a
four-dimensional gauge theory along which the conformal central charge 'a'
increases. The flow connects the maximally superconformal point of an N=2 gauge
theory with gauge group SU(N+1) and N_f=2N flavors in the ultraviolet, to a
strongly-coupled superconformal point of the SU(N) gauge theory with N_f=2N
massless flavors in the infrared. Our example does not contradict the proof of
the a-theorem via a-maximization, due to the presence of accidental symmetries
in the infrared limit. Nor does it contradict the holographic a-theorem,
because these gauge theories do not possess weakly-curved holographic duals.Comment: 22 pages, 4 figures. v3: The conclusion in the previous version was
superseded. Please refer to the abstract for the detail
Skyrmions and Hall Transport
We derive a generalized set of Ward identities that captures the effects of
topological charge on Hall transport. The Ward identities follow from the 2+1
dimensional momentum algebra, which includes a central extension proportional
to the topological charge density. In the presence of topological objects like
Skyrmions, we observe that the central term leads to a direct relation between
the thermal Hall conductivity and the topological charge density. We extend
this relation to incorporate the effects of a magnetic field and an electric
current. The topological charge density produces a distinct signature in the
electric Hall conductivity, which is identified in existing experimental data,
and yields further novel predictions. For insulating materials with translation
invariance, the Hall viscosity can be directly determined from the Skyrmion
density and the thermal Hall conductivity to be measured as a function of
momentum.Comment: 6+1 pages including Supplemental Material. Version to appear in
Physical Review Letter
On Dumb Holes and their Gravity Duals
Inhomogeneous fluid flows which become supersonic are known to produce
acoustic analogs of ergoregions and horizons. This leads to Hawking-like
radiation of phonons with a temperature essentially given by the gradient of
the velocity at the horizon. We find such acoustic dumb holes in charged
conformal fluids and use the fluid-gravity correspondence to construct dual
gravity solutions. A class of quasinormal modes around these gravitational
backgrounds perceive a horizon. Upon quantization, this implies a thermal
spectrum for these modes.Comment: 24 pages, 4 figure
Central charges of N=2 superconformal field theories in four dimensions
We present a general method for computing the central charges a and c of N=2
superconformal field theories corresponding to singular points in the moduli
space of N=2 gauge theories. Our method relates a and c to the U(1)_R anomalies
of the topologically twisted gauge theory. We evaluate these anomalies by
studying the holomorphic dependence of the path integral measure on the moduli.
We calculate a and c for superconformal points in a variety of gauge theories,
including N=4 SU(N), N=2 pure SU(N) Yang-Mills, and USp(2N) with 1 massless
antisymmetric and 4 massive fundamental hypermultiplets. In the latter case, we
reproduce the conformal and flavor central charges previously calculated using
the gravity duals of these gauge theories. For any SCFT in the class under
consideration, we derive a previously conjectured expression for 2a-c in terms
of the sum of the dimensions of operators parameterizing the Coulomb branch.
Finally, we prove that the ratio a/c is bounded above by 5/4 and below by 1/2.Comment: 38 pages, 1 figure; v2: References added, a minor error corrected.
Published versio
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