Conformal Janus on Euclidean Sphere

We interpret Janus as an interface in a conformal field theory and study its properties. The Janus is created by an exactly marginal operator and we study its effect on the interface conformal field theory on the Janus. We do this by utilizing the AdS/CFT correspondence. We compute the interface free energy both from leading correction to the Euclidean action in the dual gravity description and from conformal perturbation theory in the conformal field theory. We find that the two results agree each other and that the interface free energy scales precisely as expected from the conformal invariance of the Janus interface.Comment: 37 pages, 5 figures, references added, section 2 and references added, published versio

Higher Spin de Sitter Holography from Functional Determinants

We discuss further aspects of the higher spin dS/CFT correspondence. Using a recent result of Dunne and Kirsten, it is shown how to numerically compute the partition function of the free Sp(N) model for a large class of SO(3) preserving deformations of the flat/round metric on R^3/S^3 and the source of the spin-zero single-trace operator dual to the bulk scalar. We interpret this partition function as a Hartle-Hawking wavefunctional. It has a local maximum about the pure de Sitter vacuum. Restricting to SO(3) preserving deformations, other local maxima (which exceed the one near the de Sitter vacuum) can peak at inhomogeneous and anisotropic values of the late time metric and scalar profile. Numerical experiments suggest the remarkable observation that, upon fixing a certain average of the bulk scalar profile at I^+, the wavefunction becomes normalizable in all the other (infinite) directions of the deformation. We elucidate the meaning of double trace deformations in the context of dS/CFT as a change of basis and as a convolution. Finally, we discuss possible extensions of higher spin de Sitter holography by coupling the free theory to a Chern-Simons term.Comment: 30 pages plus appendices; v2 references adde

Geometry of logarithmic strain measures in solid mechanics

We consider the two logarithmic strain measures$$\omega_{\rm iso}=\|\mathrm{dev}_n\log U\|=\|\mathrm{dev}_n\log \sqrt{F^TF}\|\quad\text{ and }\quad \omega_{\rm vol}=|\mathrm{tr}(\log U)|=|\mathrm{tr}(\log\sqrt{F^TF})|\,,$$which are isotropic invariants of the Hencky strain tensor $\log U$, and show that they can be uniquely characterized by purely geometric methods based on the geodesic distance on the general linear group $\mathrm{GL}(n)$. Here, $F$ is the deformation gradient, $U=\sqrt{F^TF}$ is the right Biot-stretch tensor, $\log$ denotes the principal matrix logarithm, $\|.\|$ is the Frobenius matrix norm, $\mathrm{tr}$ is the trace operator and $\mathrm{dev}_n X$ is the $n$-dimensional deviator of $X\in\mathbb{R}^{n\times n}$. This characterization identifies the Hencky (or true) strain tensor as the natural nonlinear extension of the linear (infinitesimal) strain tensor $\varepsilon=\mathrm{sym}\nabla u$, which is the symmetric part of the displacement gradient $\nabla u$, and reveals a close geometric relation between the classical quadratic isotropic energy potential $$\mu\,\|\mathrm{dev}_n\mathrm{sym}\nabla u\|^2+\frac{\kappa}{2}\,[\mathrm{tr}(\mathrm{sym}\nabla u)]^2=\mu\,\|\mathrm{dev}_n\varepsilon\|^2+\frac{\kappa}{2}\,[\mathrm{tr}(\varepsilon)]^2$$in linear elasticity and the geometrically nonlinear quadratic isotropic Hencky energy$$\mu\,\|\mathrm{dev}_n\log U\|^2+\frac{\kappa}{2}\,[\mathrm{tr}(\log U)]^2=\mu\,\omega_{\rm iso}^2+\frac\kappa2\,\omega_{\rm vol}^2\,,$$where $\mu$ is the shear modulus and $\kappa$ denotes the bulk modulus. Our deduction involves a new fundamental logarithmic minimization property of the orthogonal polar factor $R$, where $F=R\,U$ is the polar decomposition of $F$. We also contrast our approach with prior attempts to establish the logarithmic Hencky strain tensor directly as the preferred strain tensor in nonlinear isotropic elasticity

Quantum Information Metric on R×Sd−1\mathbb{R} \times S^{d-1}

We present a formula for the information metric on $\mathbb{R} \times {S}^{d-1}$ for a scalar primary operator of integral dimension $\Delta \, (\,\, > \frac{d+1}{2})$. This formula is checked for various space-time dimensions $d$ and $\Delta$ in the field theory side. We check the formula in the gravity side using the holographic setup. We clarify the regularization and renormalization involved in these computations. We also show that the quantum information metric of an exactly marginal operator agrees with the leading order of the interface free energy of the conformal Janus on Euclidean ${S}^d$, which is checked for $d=2, 3$.Comment: 21 pages, 2 figure

F-Theorem without Supersymmetry

The conjectured F-theorem for three-dimensional field theories states that the finite part of the free energy on S^3 decreases along RG trajectories and is stationary at the fixed points. In previous work various successful tests of this proposal were carried out for theories with {\cal N}=2 supersymmetry. In this paper we perform more general tests that do not rely on supersymmetry. We study perturbatively the RG flows produced by weakly relevant operators and show that the free energy decreases monotonically. We also consider large N field theories perturbed by relevant double trace operators, free massive field theories, and some Chern-Simons gauge theories. In all cases the free energy in the IR is smaller than in the UV, consistent with the F-theorem. We discuss other odd-dimensional Euclidean theories on S^d and provide evidence that (-1)^{(d-1)/2} \log |Z| decreases along RG flow; in the particular case d=1 this is the well-known g-theorem.Comment: 34 pages, 2 figures; v2 refs added, minor improvements; v3 refs added, improved section 4.3; v4 minor improvement

Closed strings from decaying D-branes

We compute the emission of closed string radiation from homogeneous rolling tachyons. For an unstable decaying D$p$-brane the radiated energy is infinite to leading order for $p\leq 2$ and finite for $p>2$. The closed string state produced by a decaying brane is closely related to the state produced by D-instantons at a critical Euclidean distance from $t=0$. In the case of a D0 brane one can cutoff this divergence so that we get a finite energy final state which would be the state that the brane decays into.Comment: harvmac, 30 pages, 2 figures. v3: Improved discussion for non compact brane