16 research outputs found
Entropy of conformal perturbation defects
We consider perturbation defects obtained by perturbing a 2D conformal field
theory (CFT) by a relevant operator on a half-plane. If the perturbed bulk
theory flows to an infrared fixed point described by another CFT, the defect
flows to a conformal defect between the ultraviolet and infrared fixed point
CFTs. For short bulk renormalization group flows connecting two fixed points
which are close in theory space we find a universal perturbative formula for
the boundary entropy of the corresponding conformal perturbation defect. We
compare the value of the boundary entropy that our formula gives for the flows
between nearby Virasoro minimal models Mm with the boundary entropy of the
defect constructed by Gaiotto in [1] and find a match at the first two orders
in the 1/m expansion.Comment: 24 pages, 2 figure
Double Trace Interfaces
We introduce and study renormalization group interfaces between two
holographic conformal theories which are related by deformation by a scalar
double trace operator. At leading order in the 1/N expansion, we derive
expressions for the two point correlation functions of the scalar, as well as
the spectrum of operators living on the interface. We also compute the
interface contribution to the sphere partition function, which in two
dimensions gives the boundary g factor. Checks of our proposal include
reproducing the g factor and some defect overlap coefficients of Gaiotto's RG
interfaces at large N, and the two-point correlation function whenever
conformal perturbation theory is valid.Comment: 59 pages, 2 figure
Precise lower bound on Monster brane boundary entropy
In this paper we develop further the linear functional method of deriving
lower bounds on the boundary entropy of conformal boundary conditions in 1+1
dimensional conformal field theories (CFTs). We show here how to use detailed
knowledge of the bulk CFT spectrum. Applying the method to the Monster CFT with
c=\bar c=24 we derive a lower bound s > - 3.02 x 10^{-19} on the boundary
entropy s=ln g, and find compelling evidence that the optimal bound is s>= 0.
We show that all g=1 branes must have the same low-lying boundary spectrum,
which matches the spectrum of the known g=1 branes, suggesting that the known
examples comprise all possible g=1 branes, and also suggesting that the bound
s>= 0 holds not just for critical boundary conditions but for all boundary
conditions in the Monster CFT. The same analysis applied to a second bulk CFT
-- a certain c=2 Gaussian model -- yields a less strict bound, suggesting that
the precise linear functional bound on s for the Monster CFT is exceptional.Comment: 1+18 page
Bounds for State Degeneracies in 2D Conformal Field Theory
In this note we explore the application of modular invariance in
2-dimensional CFT to derive universal bounds for quantities describing certain
state degeneracies, such as the thermodynamic entropy, or the number of
marginal operators. We show that the entropy at inverse temperature 2 pi
satisfies a universal lower bound, and we enumerate the principal obstacles to
deriving upper bounds on entropies or quantum mechanical degeneracies for fully
general CFTs. We then restrict our attention to infrared stable CFT with
moderately low central charge, in addition to the usual assumptions of modular
invariance, unitarity and discrete operator spectrum. For CFT in the range
c_left + c_right < 48 with no relevant operators, we are able to prove an upper
bound on the thermodynamic entropy at inverse temperature 2 pi. Under the same
conditions we also prove that a CFT can have a number of marginal deformations
no greater than ((c_left + c_right) / (48 - c_left - c_right)) e^(4 Pi) - 2.Comment: 23 pages, LaTeX, minor change
Bulk flows in Virasoro minimal models with boundaries
The behaviour of boundary conditions under relevant bulk perturbations is
studied for the Virasoro minimal models. In particular, we consider the bulk
deformation by the least relevant bulk field which interpolates between the mth
and (m-1)st unitary minimal model. In the presence of a boundary this bulk flow
induces an RG flow on the boundary, which ensures that the resulting boundary
condition is conformal in the (m-1)st model. By combining perturbative RG
techniques with insights from defects and results about non-perturbative
boundary flows, we determine the endpoint of the flow, i.e. the boundary
condition to which an arbitrary boundary condition of the mth theory flows to.Comment: 34 pages, 6 figures. v4: Typo in fig. 2 correcte