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

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 $\Delta\leq0.19$. This means in particular that unlike the second Renyi entropy, the third one is no longer universal.Comment: 28 pages + Appendice

Continuous-wave, multimilliwatt, mid-infrared source tunable across 6.4–7.5 μm based on orientation-patterned GaAs

We report a continuous-wave (cw) source of tunable mid-infrared radiation providing tens of milliwatt of output power in the 6460–7517 nm spectral range. The source is based on difference-frequency generation (DFG) in orientation-patterned (OP)-GaAs pumped by a Tm-fiber laser at 2010 nm and a 1064 nm-Yb-fiber-pumped cw optical parametric oscillator. Using a 25.7-mm-long OP-GaAs crystal, we have generated up to 51.1 mW of output power at 6790 nm, with >40 mW and >20 mW across 32% and 80% of the mid-infrared tuning range, respectively, which is to the best of our knowledge the highest tunable cw power generated in OP-GaAs in this spectral range. The DFG output at maximum power exhibits passive power stability better than 2.3% rms over more than 1 h and a frequency stability of 1.8 GHz over more than 1 min, in high spatial beam quality. The system and crystal performance at high pump powers have been studiedPostprint (published version

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 $W_\infty$ 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

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