32 research outputs found
Lifting 1/4-BPS States on K3 and Mathieu Moonshine
The elliptic genus of K3 is an index for the 1/4-BPS states of its sigma
model. At the torus orbifold point there is an accidental degeneracy of such
states. We blow up the orbifold fixed points using conformal perturbation
theory, and find that this fully lifts the accidental degeneracy of the 1/4-BPS
states with h=1. At a generic point near the Kummer surface the elliptic genus
thus measures not just their index, but counts the actual number of these BPS
states. We comment on the implication of this for symmetry surfing and Mathieu
moonshine.Comment: 29+5 pp, a sign mistake corrected in eqs. (3.14) and (4.20), footnote
6 added to clarify this point, references adde
Lifting of D1-D5-P states
We consider states of the D1-D5 CFT where only the left-moving sector is
excited. As we deform away from the orbifold point, some of these states will
remain BPS while others can `lift'. We compute this lifting for a particular
family of D1-D5-P states, at second order in the deformation off the orbifold
point. We note that the maximally twisted sector of the CFT is special: the
covering surface appearing in the correlator can only be genus one while for
other sectors there is always a genus zero contribution. We use the results to
argue that fuzzball configurations should be studied for the full class
including both extremal and near-extremal states; many extremal configurations
may be best seen as special limits of near extremal configurations.Comment: 51 pages, 6 figure
Higgsing the stringy higher spin symmetry
It has recently been argued that the symmetric orbifold theory of T4 is dual
to string theory on AdS3 x S3 x T4 at the tensionless point. At this point in
moduli space, the theory possesses a very large symmetry algebra that includes,
in particular, a algebra capturing the gauge fields of a dual higher
spin theory. Using conformal perturbation theory, we study the behaviour of the
symmetry generators of the symmetric orbifold theory under the deformation that
corresponds to switching on the string tension. We show that the generators
fall nicely into Regge trajectories, with the higher spin fields corresponding
to the leading Regge trajectory. We also estimate the form of the Regge
trajectories for large spin, and find evidence for the familiar logarithmic
behaviour, thereby suggesting that the symmetric orbifold theory is dual to an
AdS background with pure RR flux.Comment: 27 pages, 1 figure, note added in version
Genus Two Partition Functions and Renyi Entropies of Large c CFTs
We compute genus two partition functions in two dimensional conformal field
theories at large central charge, focusing on surfaces that give the third
Renyi entropy of two intervals. We compute this for generalized free theories
and for symmetric orbifolds, and compare it to the result in pure gravity. We
find a new phase transition if the theory contains a light operator of
dimension . This means in particular that unlike the second
Renyi entropy, the third one is no longer universal.Comment: 28 pages + Appendice
Renyi Entropies, the Analytic Bootstrap, and 3D Quantum Gravity at Higher Genus
We compute the contribution of the vacuum Virasoro representation to the
genus-two partition function of an arbitrary CFT with central charge .
This is the perturbative pure gravity partition function in three dimensions.
We employ a sewing construction, in which the partition function is expressed
as a sum of sphere four-point functions of Virasoro vacuum descendants. For
this purpose, we develop techniques to efficiently compute correlation
functions of holomorphic operators, which by crossing symmetry are determined
exactly by a finite number of OPE coefficients; this is an analytic
implementation of the conformal bootstrap. Expanding the results in ,
corresponding to the semiclassical bulk gravity expansion, we find
that---unlike at genus one---the result does not truncate at finite loop order.
Our results also allow us to extend earlier work on multiple-interval Renyi
entropies and on the partition function in the separating degeneration limit.Comment: 63 pages + ref