36 research outputs found
A test of bosonization at the level of four-point functions in Chern-Simons vector models
We study four-point functions in Chern-Simons vector models in the large
limit. We compute the four-point function of the scalar primary to all orders
in the `t Hooft coupling in Chern-Simons theory coupled
to a fundamental fermion, in both the critical and non-critical theory, for a
particular case of the external momenta. These theories cover the entire
3-parameter "quasi-boson" and 2-parameter "quasi-fermion" families of
3-dimensional quantum field theories with a slightly-broken higher spin
symmetry. Our results are consistent with the celebrated bosonization duality,
as we explicitly verify by calculating four-point functions in the free
critical and non-critical bosonic theories.Comment: 20 pages, various improvement
Anomalous Dimensions in Non-Supersymmetric Bifundamental Chern-Simons Theories
Non-abelian Chern-Simons theories coupled to fermions are known to provide an
interesting class of non-supersymmetric conformal fixed points
\cite{Giombi:2011kc}. These theories, particularly those based on bifundamental
matter, are important because they may provide simple non-supersymmetric
examples of the AdS/CFT correspondence. For instance, it seems natural to
conjecture that Chern-Simons theory coupled to
Majorana fermions transforming in a bi-vector representation may be dual to
pure Einstein gravity with a small negative cosmological constant in the
"M-theory" limit where and is large. While it is extremely difficult
to directly study such bifundamental theories when or even at strong 't
Hooft coupling , it is possible to calculate physical
quantities to all orders in in a
theory, in the limit , in an expansion. To illustrate this, we
calculate the anomalous dimension of the primary operator ,
to first order in , to all orders in , but with
. We also comment on possible bosonization dualities
for bifundamental Chern-Simons theories.Comment: 16 pages; v5: added correction
Bootstrap and collider physics of parity violating conformal field theories in
We study the crossing equations in for the four point function of two
currents and two scalars including the presence of a parity violating
term for the -channel stress tensor exchange. We show the existence of a new
tower of double trace operators in the -channel whose presence is necessary
for the crossing equation to be satisfied and determine the corresponding large
spin parity violating OPE coefficients. Contrary to the parity even situation,
we find that the parity odd -channel light cone stress tensor block do not
have logarithmic singularities. This implies that the parity odd term does not
contribute to anomalous dimensions in the crossed channel at this order in
light cone expansion. We then study the constraints imposed by reflection
positivity and crossing symmetry on such a four point function. We reproduce
the previously known parity odd collider bounds through this analysis. The
contribution of the parity violating term in the collider bound results from a
square root branch cut present in the light cone block as opposed to a
logarithmic cut in the parity even case, together with the application of the
Cauchy-Schwarz inequality.Comment: References update
Emergent Supersymmetry at Large
We search for infrared fixed points of Gross-Neveu Yukawa models with matrix
degrees of freedom in . We consider three models -- a model
with symmetry in which the scalar and fermionic fields both transform
in the adjoint representation, a model with symmetry in which the
scalar and fermion fields both transform as real symmetric-traceless matrices,
and a model with symmetry in which the scalar field transforms as a
real symmetric-traceless matrix, while the fermion transforms in the adjoint
representation. These models differ at finite , but their large- limits
are perturbatively equivalent. The first two models contain a supersymmetric
fixed point for all , which is attractive to all classically-marginal
deformations for sufficiently large. The third model possesses a fixed
point that, although non-supersymmetric for any finite , possesses emergent
supersymmetry when is sufficiently large. We also find several
non-supersymmetric fixed points at finite and large-. Planar diagrams
dominate the large- limit of these fixed points, which suggests the
possibility of a stringy holographic dual description.Comment: 80 pages, 19 figure
Spectral sum rules for conformal field theories in arbitrary dimensions
We derive spectral sum rules in the shear channel for conformal field
theories at finite temperature in general dimensions. The sum rules
result from the OPE of the stress tensor at high frequency as well as the
hydrodynamic behaviour of the theory at low frequencies. The sum rule states
that a weighted integral of the spectral density over frequencies is
proportional to the energy density of the theory. We show that the
proportionality constant can be written in terms the Hofman-Maldacena variables
which determine the three point function of the stress tensor. For
theories which admit a two derivative gravity dual this proportionality
constant is given by . We then use causality constraints and
obtain bounds on the sum rule which are valid in any conformal field theory.
Finally we demonstrate that the high frequency behaviour of the spectral
function in the vector and the tensor channel are also determined by the
Hofman-Maldacena variables.Comment: Corrected typos, JHEP versio
Constraints on parity violating conformal field theories in
We derive constraints on three-point functions involving the stress tensor,
, and a conserved current, , in 2+1 dimensional conformal field
theories that violate parity, using conformal collider bounds introduced by
Hofman and Maldacena. Conformal invariance allows parity-odd tensor-structures
for the and correlation
functions which are unique to three space-time dimensions. Let the parameters
which determine the correlation function be and
, where is the parity-violating contribution. Similarly
let the parameters which determine correlation
function be , and , where is the parity-violating
contribution. We show that the parameters and are bounded to lie inside a disc at the origin of the -
plane and the - plane respectively. We then show
that large Chern-Simons theories coupled to a fundamental fermion/boson lie
on the circle which bounds these discs. The `t Hooft coupling determines the
location of these theories on the boundary circles.Comment: Minor typos corrected, Figures changed , References adde