Phase Structure of Higher Spin Black Holes

We revisit the study of the phase structure of higher spin black holes carried out in arXiv$:1210.0284$ using the "canonical formalism". In particular we study the low as well as high temperature regimes. We show that the Hawking-Page transition takes place in the low temperature regime. The thermodynamically favoured phase changes from conical surplus to black holes and then again to conical surplus as we increase temperature. We then show that in the high temperature regime the diagonal embedding gives the appropriate description. We also give a map between the parameters of the theory near the IR and UV fixed points. This makes the "good" solutions near one end map to the "bad" solutions near the other end and vice versa.Comment: References added, Conclusions written in better manner, overall exposition improved, version accepted in JHE

Open Boundary Condition, Wilson Flow and the Scalar Glueball Mass

A major problem with periodic boundary condition on the gauge fields used in current lattice gauge theory simulations is the trapping of topological charge in a particular sector as the continuum limit is approached. To overcome this problem open boundary condition in the temporal direction has been proposed recently. One may ask whether open boundary condition can reproduce the observables calculated with periodic boundary condition. In this work we find that the extracted lowest glueball mass using open and periodic boundary conditions at the same lattice volume and lattice spacing agree for the range of lattice scales explored in the range 3 GeV $\leq$ 1/a $\leq$ 5 GeV. The problem of trapping is overcome to a large extent with open boundary and we are able to extract the glueball mass at even larger lattice scale $\approx$ 5.7 GeV. To smoothen the gauge fields and to reduce the cut off artifacts recently proposed Wilson flow is used. The extracted glueball mass shows remarkable insensitivity to the lattice spacings in the range explored in this work, 3 GeV $\leq$ 1/a $\leq$ 5.7 GeV.Comment: Replacement agrees with published versio

S-duality invariant perturbation theory improved by holography

We study anomalous dimensions of unprotected low twist operators in the four-dimensional $SU(N)$ $\mathcal{N}=4$ supersymmetric Yang-Mills theory. We construct a class of interpolating functions to approximate the dimensions of the leading twist operators for arbitrary gauge coupling $\tau$. The interpolating functions are consistent with previous results on the perturbation theory, holographic computation and full S-duality. We use our interpolating functions to test a recent conjecture by the $\mathcal{N}=4$ superconformal bootstrap that upper bounds on the dimensions are saturated at one of the duality-invariant points $\tau =i$ and $\tau =e^{i\pi /3}$. It turns out that our interpolating functions have maximum at $\tau =e^{i\pi /3}$, which are close to the conjectural values by the conformal bootstrap. In terms of the interpolating functions, we draw the image of conformal manifold in the space of the dimensions. We find that the image is almost a line despite the conformal manifold is two-dimensional. We also construct interpolating functions for the subleading twist operator and study level crossing phenomenon between the leading and subleading twist operators. Finally we study the dimension of the Konishi operator in the planar limit. We find that our interpolating functions match with numerical result obtained by Thermodynamic Bethe Ansatz very well. It turns out that analytic properties of the interpolating functions reflect an expectation on a radius of convergence of the perturbation theory.Comment: 39+14 pages, 22 figures; v3: minor correction

Topological susceptibility in lattice Yang-Mills theory with open boundary condition

We find that using open boundary condition in the temporal direction can yield the expected value of the topological susceptibility in lattice SU(3) Yang-Mills theory. As a further check, we show that the result agrees with numerical simulations employing the periodic boundary condition. Our results support the preferability of the open boundary condition over the periodic boundary condition as the former allows for computation at smaller lattice spacings needed for continuum extrapolation at a lower computational cost.Comment: One figure added, replacement agrees with the published versio