Superconformal index for large N quiver Chern-Simons theories

We investigate the N=2 superconformal index for supersymmetric quiver Chern-Simons theories with large N gauge groups. After general arguments about the large N limit, we compute the first few terms in the series expansion of the index for theories proposed as dual theories to homogeneous spaces V^{5,2}, Q^{1,1,1}, Q^{2,2,2}, M^{1,1,1}, and N^{0,1,0}. We confirm that the indices have symmetries expected from the isometries of dual manifolds.Comment: 27 pages, 7 figures; v2: typos corrected, Sec.6 modified; v3: explanation improved, minor corrections, version published in JHE

N=2 supersymmetric theories on squashed three-sphere

We investigate a squashing deformation of 3d N=2 supersymmetric theories on three-sphere, which have four supercharges. The deformation preserves SU(2)_L x U(1)_r isometry and all four supersymmetries. We compute the partition function and find non-trivial dependence on the squashing parameter. We also consider the large N limit of a certain class of quiver gauge theories which have free energy of order N^{3/2}, and show that the free energy on the squashed sphere differs from that on round sphere by a certain factor depending only on the squashing parameter.Comment: 39 pages, 2 figures, v2: minor corrections, references added; v3: minor correction

Geometric free energy of toric AdS4/CFT3 models

We study the supersymmetric free energy of three dimensional Chern-Simons-matter theories holographically dual to AdS$_4$ times toric Sasaki-Einstein seven-manifolds. In the large $N$ limit, we argue that the square of the free energy can be written as a quartic polynomial of trial R-charges. The coefficients of the polynomial are determined geometrically from the toric diagrams. We present the coefficients of the quartic polynomial explicitly for generic toric diagrams with up to 6 vertices, and some particular diagrams with 8 vertices. Decomposing the trial R-charges into mesonic and baryonic variables, and eliminating the baryonic ones, we show that the quartic polynomial reproduces the inverse of the Martelli-Sparks-Yau volume function. On the gravity side, we explore the possibility of using the same quartic polynomial as the prepotential in the AdS gauged supergravity. Comparing Kaluza-Klein gravity and gauged supergravity descriptions, we find perfect agreement in the mesonic sector but some discrepancy in the baryonic sector.Comment: 39 pages, 21 figures; v2. references added, minor improvement

Parity Violation of Gravitons in the CMB Bispectrum

We investigate the cosmic microwave background (CMB) bispectra of the intensity (temperature) and polarization modes induced by the graviton non-Gaussianities, which arise from the parity-conserving and parity-violating Weyl cubic terms with time-dependent coupling. By considering the time-dependent coupling, we find that even in the exact de Sitter space time, the parity violation still appears in the three-point function of the primordial gravitational waves and could become large. Through the estimation of the CMB bispectra, we demonstrate that the signals generated from the parity-conserving and parity-violating terms appear in completely different configurations of multipoles. For example, the parity-conserving non-Gaussianity induces the nonzero CMB temperature bispectrum in the configuration with $\sum_{n=1}^3 \ell_n = {\rm even}$ and, while due to the parity-violating non-Gaussianity, the CMB temperature bispectrum also appears for $\sum_{n=1}^3 \ell_n = {\rm odd}$. This signal is just good evidence of the parity violation in the non-Gaussianity of primordial gravitational waves. We find that the shape of this non-Gaussianity is similar to the so-called equilateral one and the amplitudes of these spectra at large scale are roughly estimated as $|b_{\ell \ell \ell}| \sim \ell^{-4} \times 3.2 \times 10^{-2} ({\rm GeV} / \Lambda)^2 (r / 0.1)^4$, where $\Lambda$ is an energy scale that sets the magnitude of the Weyl cubic terms (higher derivative corrections) and $r$ is a tensor-to-scalar ratio. Taking the limit for the nonlinearity parameter of the equilateral type as $f_{\rm NL}^{\rm eq} < 300$, we can obtain a bound as $\Lambda \gtrsim 3 \times 10^6 {\rm GeV}$, assuming $r=0.1$.Comment: 23 pages, 3 figures. Accepted for publication in PTP. Version 3 includes errata in Fig.

Supersymmetry Enhancement and Junctions in S-folds

We study supersymmetry enhancement from ${\cal N}=3$ to ${\cal N}=4$ proposed by Aharony and Tachikawa by using string junctions in S-folds. The central charges carried by junctions play a central role in our analysis. We consider planer junctions in a specific plane. Before the S-folding they carry two complex central charges, which we denote by $Z$ and $\bar Z$. The S-fold projection eliminates $\bar Z$ as well as one of the four supercharges, and when the supersymmetry is enhanced $\bar Z$ should be reproduced by some non-perturbative mechanism. For the models of $\mathbb{Z}_3$ and $\mathbb{Z}_4$ S-folds which are expected to give $SU(3)$ and $SO(5)$ ${\cal N}=4$ theories we compare the junction spectra with those in perturbative brane realization of the same theories. We establish one-to-one correspondence so that $Z$ coincides. By using the correspondence we also give an expression for the enhanced central charge $\bar Z$.Comment: 30 pages, 7 figures, v2: minor corrections, version accepted for publication in JHE

Constraining modified theory of gravity with galaxy bispectrum

We explore the use of galaxy bispectrum induced by the nonlinear gravitational evolution as a possible probe to test general scalar-tensor theories with second-order equations of motion. We find that time dependence of the leading second-order kernel is approximately characterized by one parameter, the second-order index, which is expected to trace the higher-order growth history of the Universe. We show that our new parameter can significantly carry new information about the non-linear growth of structure. We forecast future constraints on the second-order index as well as the equation-of-state parameter and the growth index.Comment: 15 pages, 2 figure