A study of symmetry breaking in a relativistic Bose gas using the contraction algorithm

A relativistic Bose gas at finite density suffers from a sign problem that makes direct numerical simulations not feasible. One possible solution to the sign problem is to re-express the path integral in terms of Lefschetz thimbles. Using this approach we study the relativistic Bose gas both in the symmetric phase (low-density) and the spontaneously broken phase (high-density). In the high-density phase we break explicitly the symmetry and determine the dependence of the order parameter on the breaking. We study the relative contributions of the dominant and sub-dominant thimbles in this phase. We find that the sub-dominant thimble only contributes substantially when the explicit symmetry breaking is small, a regime that is dominated by finite volume effects. In the regime relevant for the thermodynamic limit, this contribution is negligible.Comment: 12 pages, 6 figures, 1 tabl

Fast Estimator of jacobians in Monte Carlo Integration on Lefschetz Thimbles

A solution to the sign problem is the so-called "Lefschetz thimble approach" where the domain of integration for field variables in the path integral is deformed from the real axis to a sub-manifold in the complex space. For properly chosen sub-manifolds ("thimbles") the sign problem disappears or is drastically alleviated. The parametrization of the thimble by real coordinates require the calculation of a jacobian with a computational cost of order O(V^3), where V is proportional to the spacetime volume. In this note we propose two estimators for this jacobian with a computational cost of order O(V). We discuss analytically the regimes where we expect the estimator to work and show numerical examples in two different models.Comment: 10 pages, 3 figure

A note on a gauge-gravity relation and functional determinants

We present a refinement of a recently found gauge-gravity relation between one-loop effective actions: on the gauge side, for a massive charged scalar in 2d dimensions in a constant maximally symmetric electromagnetic field; on the gravity side, for a massive spinor in d-dimensional (Euclidean) anti-de Sitter space. The inclusion of the dimensionally regularized volume of AdS leads to complete mapping within dimensional regularization. In even-dimensional AdS, we get a small correction to the original proposal; whereas in odd-dimensional AdS, the mapping is totally new and subtle, with the `holographic trace anomaly' playing a crucial role.Comment: 6 pages, io

Chiral Modulations in Curved Space I: Formalism

The goal of this paper is to present a formalism that allows to handle four-fermion effective theories at finite temperature and density in curved space. The formalism is based on the use of the effective action and zeta function regularization, supports the inclusion of inhomogeneous and anisotropic phases. One of the key points of the method is the use of a non-perturbative ansatz for the heat-kernel that returns the effective action in partially resummed form, providing a way to go beyond the approximations based on the Ginzburg-Landau expansion for the partition function. The effective action for the case of ultra-static Riemannian spacetimes with compact spatial section is discussed in general and a series representation, valid when the chemical potential satisfies a certain constraint, is derived. To see the formalism at work, we consider the case of static Einstein spaces at zero chemical potential. Although in this case we expect inhomogeneous phases to occur only as meta-stable states, the problem is complex enough and allows to illustrate how to implement numerical studies of inhomogeneous phases in curved space. Finally, we extend the formalism to include arbitrary chemical potentials and obtain the analytical continuation of the effective action in curved space.Comment: 22 pages, 3 figures; version to appear in JHE

Determinant and Weyl anomaly of Dirac operator: a holographic derivation

We present a holographic formula relating functional determinants: the fermion determinant in the one-loop effective action of bulk spinors in an asymptotically locally AdS background, and the determinant of the two-point function of the dual operator at the conformal boundary. The formula originates from AdS/CFT heuristics that map a quantum contribution in the bulk partition function to a subleading large-N contribution in the boundary partition function. We use this holographic picture to address questions in spectral theory and conformal geometry. As an instance, we compute the type-A Weyl anomaly and the determinant of the iterated Dirac operator on round spheres, express the latter in terms of Barnes' multiple gamma function and gain insight into a conjecture by B\"ar and Schopka.Comment: 11 pages; new comments and references added, typos correcte

Views of the Chiral Magnetic Effect

My personal views of the Chiral Magnetic Effect are presented, which starts with a story about how we came up with the electric-current formula and continues to unsettled subtleties in the formula. There are desirable features in the formula of the Chiral Magnetic Effect but some considerations would lead us to even more questions than elucidations. The interpretation of the produced current is indeed very non-trivial and it involves a lot of confusions that have not been resolved.Comment: 19 pages, no figure; typos corrected, references significantly updated, to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye

Evidence for B cell exhaustion in chronic graft-versus-host disease

Chronic graft-versus-host disease (cGvHD) remains a major complication of allogeneic hematopoietic stem cell transplantation (HSCT). A number of studies support a role for B cells in the pathogenesis of cGvHD. In this study, we report the presence of an expanded population of CD19+CD21− B cells with features of exhaustion in the peripheral blood of patients with cGvHD. CD21− B cells were significantly increased in patients with active cGvHD compared to patients without cGvHD and healthy controls (median 12.2 versus 2.12 versus 3%, respectively; p < 0.01). Compared with naïve (CD27−CD21+) and classical memory (CD27+CD21+) B cells, CD19+CD21− B cells in cGvHD were CD10 negative, CD27 negative and CD20hi, and exhibited features of exhaustion, including increased expression of multiple inhibitory receptors such as FCRL4, CD22, CD85J, and altered expression of chemokine and adhesion molecules such as CD11c, CXCR3, CCR7, and CD62L. Moreover, CD21− B cells in cGvHD patients were functionally exhausted and displayed poor proliferative response and calcium mobilization in response to B-cell receptor triggering and CD40 ligation. Finally, the frequencies of circulating CD21− B cells correlated with cGvHD severity in patients after HSCT. Our study further characterizes B cells in chronic cGVHD and supports the use of CD21−CD27−CD10− B cell frequencies as a biomarker of disease severity

Chern-Simons diffusion rate in a holographic Yang-Mills theory

Using holography, we compute the Chern-Simons diffusion rate of 4d gauge theories constructed by wrapping D4-branes on a circle. In the model with antiperiodic boundary conditions for fermions, we find that it scales like $T^6$ in the high-temperature phase. With periodic fermions, this scaling persists at low temperatures. The scaling is reminiscent of 6d hydrodynamic behavior even at temperatures small compared to compactification scales of the M5-branes from which the D4-branes descend. We offer a holographic explanation of this behavior by adding a new entry to the known map between D4 and M5 hydrodynamics, and suggest a field theory explanation based on "deconstruction" or "fractionization".Comment: 13 pages, misstatement in published version about low temperature phase removed, main results unaffecte

Export-Oriented International Joint Venture: Endogenous Set-Up Costs and Information Gathering

We analyze the formation of an export-oriented international joint venture (IJV) between a multinational corporation (MNC) and a domestic firm under demand uncertainty and in a principal-agent framework. The MNC possesses a superior production technology and is better at predicting foreign market demand. The domestic firm can reduce set-up costs of the IJV with effort levels that is endogenously determined. We examine how the MNC\u27s preference for, and the ownership structure of, a joint venture depend on the efficiency of information gathering and of cost reduction, and on the nature of credit markets. We find, inter alia, that when the credit constraint is severe the MNC does not push the domestic firm to its reservation profit level. A relaxation of the credit constraint facing the domestic firm never makes it better off and in fact makes the domestic firm worse off when the credit constraint is severe