The topologically twisted index of $$ \mathcal{N} $$ = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tail

We investigate the large-N asymptotics of the topologically twisted index of $$ \mathcal{N} $$ N = 4 SU(N) Super-Yang-Mills (SYM) theory on T2 × S2 and provide its holographic interpretation based on the black hole Farey tail [1]. In the field theory side, we use the Bethe-Ansatz (BA) formula, which gives the twisted index of $$ \mathcal{N} $$ N = 4 SYM theory as a discrete sum over Bethe vacua, to compute the large-N asymptotics of the twisted index. In a dual $$ \mathcal{N} $$ N = 2 gauged STU model, we construct a family of 5d extremal solutions uplifted from the 3d black hole Farey tail, and compute the regularized on-shell actions. The gravitational partition function given in terms of these regularized on-shell actions is then compared with a canonical partition function derived from the twisted index by the inverse Laplace transform, in the large-N limit. This extends the previous microstate counting of an AdS5 black string by the twisted index and thereby improves holographic understanding of the twisted index.

Geodesic Circular Orbits Sharing the Same Orbital Frequencies in the Black String Spacetime

We consider isofrequency pairing of geodesic orbits that share the same three orbital frequencies associated with Ωr^, Ωφ^, and Ωω^ in a particular region of parameter space around black string spacetime geometry. We study the effect of a compact extra spatial dimension on the isofrequency pairing of geodesic orbits and show that such orbits would occur in the allowed region when particles move along the black string. We find that the presence of the compact extra dimension leads to an increase in the number of the isofrequency pairing of geodesic orbits. Interestingly we also find that isofrequency pairing of geodesic orbits in the region of parameter space cannot be realized beyond the critical value Jcr≈0.096 of the conserved quantity of the motion arising from the compact extra spatial dimension.

A new spin on the Weak Gravity Conjecture

The mild form of the Weak Gravity Conjecture states that quantum or higher-derivative corrections should decrease the mass of large extremal charged black holes at fixed charge. This allows extremal black holes to decay, unless protected by a symmetry (such as supersymmetry). We reformulate this conjecture as an integrated condition on the effective stress tensor capturing the effect of quantum or higher-derivative corrections. In addition to charged black holes, we also consider rotating BTZ black holes and show that this condition is satisfied as a consequence of the c-theorem, proving a spinning version of the Weak Gravity Conjecture. We also apply our results to a five-dimensional boosted black string with higher-derivative corrections. The boosted black string has a BTZ×S2 near-horizon geometry and, after Kaluza-Klein reduction, describes a four-dimensional charged black hole. Combining the spinning and charged Weak Gravity Conjecture we obtain positivity bounds on the five-dimensional Wilson coefficients that are stronger than those obtained from charged black holes alone.

Rotating black string in Born–Infeld gravity’s rainbow

Compact objects endowed with rotation and charge are interesting both from physical and mathematical points of view. Motivated by the recent interesting consequences of gravity’s rainbow, in this paper we introduce energy-dependent asymptotically anti-de Sitter black string solutions of Einstein–Born–Infeld gravity. We report the geometric properties of the solutions and generalize them to rotating black string solutions through an improper local transformation. We calculate the conserved and thermodynamic quantities of rotating black strings and examine the validity of the first law of thermodynamics. In addition, the effects of both rainbow functions and nonlinear electrodynamics on the thermodynamic behavior of the solutions will be studied. Finally, we investigate the thermal stability of the solutions using different methods.

Anomalies of (0,4) SCFTs from F-theory

We study the macroscopics of 2d $$ \mathcal{N} $$ N = (0, 4) SCFTs arising from F-theory constructions. The class of 2d SCFTs we consider live on black strings which are obtained by wrapping D3-branes on a curve in the base of a possibly singular elliptically fibered Calabi-Yau threefold. In addition, we allow the D3-branes to probe ALE or ALF spaces transversely. We compute anomaly coefficients of these SCFTs by determining Chern- Simons terms in the 3d action resulting from the reduction of 6d $$ \mathcal{N} $$ N = (1, 0) supergravity on the compact space surrounding the black string. Essential contributions to these coefficients are from one-loop induced Chern-Simons terms arising from integrating out massive Kaluza-Klein modes.