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Quantum Effective Action in Spacetimes with Branes and Boundaries

We construct quantum effective action in spacetime with branes/boundaries. This construction is based on the reduction of the underlying Neumann type boundary value problem for the propagator of the theory to that of the much more manageable Dirichlet problem. In its turn, this reduction follows from the recently suggested Neumann-Dirichlet duality which we extend beyond the tree level approximation. In the one-loop approximation this duality suggests that the functional determinant of the differential operator subject to Neumann boundary conditions in the bulk factorizes into the product of its Dirichlet counterpart and the functional determinant of a special operator on the brane -- the inverse of the brane-to-brane propagator. As a byproduct of this relation we suggest a new method for surface terms of the heat kernel expansion. This method allows one to circumvent well-known difficulties in heat kernel theory on manifolds with boundaries for a wide class of generalized Neumann boundary conditions. In particular, we easily recover several lowest order surface terms in the case of Robin and oblique boundary conditions. We briefly discuss multi-loop applications of the suggested Dirichlet reduction and the prospects of constructing the universal background field method for systems with branes/boundaries, analogous to the Schwinger-DeWitt technique.Comment: LaTeX, 25 pages, final version, to appear in Phys. Rev.

Effective action and heat kernel in a toy model of brane-induced gravity

We apply a recently suggested technique of the Neumann-Dirichlet reduction to a toy model of brane-induced gravity for the calculation of its quantum one-loop effective action. This model is represented by a massive scalar field in the $(d+1)$-dimensional flat bulk supplied with the $d$-dimensional kinetic term localized on a flat brane and mimicking the brane Einstein term of the Dvali-Gabadadze-Porrati (DGP) model. We obtain the inverse mass expansion of the effective action and its ultraviolet divergences which turn out to be non-vanishing for both even and odd spacetime dimensionality $d$. For the massless case, which corresponds to a limit of the toy DGP model, we obtain the Coleman-Weinberg type effective potential of the system. We also obtain the proper time expansion of the heat kernel in this model associated with the generalized Neumann boundary conditions containing second order tangential derivatives. We show that in addition to the usual integer and half-integer powers of the proper time this expansion exhibits, depending on the dimension $d$, either logarithmic terms or powers multiple of one quarter. This property is considered in the context of strong ellipticity of the boundary value problem, which can be violated when the Euclidean action of the theory is not positive definite.Comment: LaTeX, 20 pages, new references added, typos correcte

Spectral action for torsion with and without boundaries

We derive a commutative spectral triple and study the spectral action for a rather general geometric setting which includes the (skew-symmetric) torsion and the chiral bag conditions on the boundary. The spectral action splits into bulk and boundary parts. In the bulk, we clarify certain issues of the previous calculations, show that many terms in fact cancel out, and demonstrate that this cancellation is a result of the chiral symmetry of spectral action. On the boundary, we calculate several leading terms in the expansion of spectral action in four dimensions for vanishing chiral parameter $\theta$ of the boundary conditions, and show that $\theta=0$ is a critical point of the action in any dimension and at all orders of the expansion.Comment: 16 pages, references adde

The Structure of Proteins: Two Hydrogen-Bonded Helical Configurations of the Polypeptide Chain

During the past fifteen years we have been attacking the problem of the structure of proteins in several ways. One of these ways is the complete and accurate determination of the crystal structure of amino acids, peptides, and other simple substances related to proteins, in order that information about interatomic distances, bond angles, and other configurational parameters might be obtained that would permit the reliable prediction of reasonable configurations for the polypeptide chain. We have now used this information to construct two reasonable hydrogen-bonded helical configurations for the polypeptide chain; we think that it is likely that these configurations constitute an important part of the structure of both fibrous and globular proteins, as well as of synthetic polypeptides. A letter announcing their discovery was published last year [1]. The problem that we have set ourselves is that of finding all hydrogen-bonded structures for a single polypeptide chain, in which the residues are equivalent (except for the differences in the side chain R). An amino acid residue (other than glycine) has no symmetry elements. The general operation of conversion of one residue of a single chain into a second residue equivalent to the first is accordingly a rotation about an axis accompanied by translation along the axis. Hence the only configurations for a chain compatible with our postulate of equivalence of the residues are helical configurations. For rotational angle 180° the helical configurations may degenerate to a simple chain with all of the principal atoms, C, C' (the carbonyl carbon), N, and O, in the same plane

Multiple reflection expansion and heat kernel coefficients

We propose the multiple reflection expansion as a tool for the calculation of heat kernel coefficients. As an example, we give the coefficients for a sphere as a finite sum over reflections, obtaining as a byproduct a relation between the coefficients for Dirichlet and Neumann boundary conditions. Further, we calculate the heat kernel coefficients for the most general matching conditions on the surface of a sphere, including those cases corresponding to the presence of delta and delta prime background potentials. In the latter case, the multiple reflection expansion is shown to be non-convergent.Comment: 21 pages, corrected for some misprint

The C_2 heat-kernel coefficient in the presence of boundary discontinuities

We consider the heat-kernel on a manifold whose boundary is piecewise smooth. The set of independent geometrical quantities required to construct an expression for the contribution of the boundary discontinuities to the C_{2} heat-kernel coefficient is derived in the case of a scalar field with Dirichlet and Robin boundary conditions. The coefficient is then determined using conformal symmetry and evaluation on some specific manifolds. For the Robin case a perturbation technique is also developed and employed. The contributions to the smeared heat-kernel coefficient and cocycle function are calculated. Some incomplete results for spinor fields with mixed conditions are also presented.Comment: 25 pages, LaTe

The ground state energy of a spinor field in the background of a finite radius flux tube

We develop a formalism for the calculation of the ground state energy of a spinor field in the background of a cylindrically symmetric magnetic field. The energy is expressed in terms of the Jost function of the associated scattering problem. Uniform asymptotic expansions needed are obtained from the Lippmann-Schwinger equation. The general results derived are applied to the background of a finite radius flux tube with a homogeneous magnetic field inside and the ground state energy is calculated numerically as a function of the radius and the flux. It turns out to be negative, remaining smaller by a factor of $\alpha$ than the classical energy of the background except for very small values of the radius which are outside the range of applicability of QED.Comment: 25 pages, 3 figure

Use of HIV Case Surveillance System to Design and Evaluate Site-Randomized Interventions in an HIV Prevention Study: HPTN 065

Introduction: Modeling studies suggest intensified HIV testing, linkage-to-care and antiretroviral treatment to achieve viral suppression may reduce HIV transmission and lead to control of the epidemic. To study implementation of strategy, population-level data are needed to monitor outcomes of these interventions. US HIV surveillance systems are a potential source of these data. Methods: HPTN065 (TLC-Plus) Study is evaluating the feasibility of a test, linkage-to-care, and treat strategy for HIV prevention in two intervention communities - the Bronx, NY, and Washington, DC. Routinely collected laboratory data on diagnosed HIV cases in the national HIV surveillance system were used to select and randomize sites, and will be used to assess trial outcomes. Results: To inform study randomization, baseline data on site-aggregated study outcomes was provided from HIV surveillance data by New York City and Washington D.C. Departments of Health. The median site rate of linkage-to-care for newly diagnosed cases was 69% (IQR 50%-86%) in the Bronx and 54% (IQR 33%-71%) in Washington, D.C. In participating HIV care sites, the median site percent of patients with viral suppression (<400 copies/mL) was 57% (IQR 53%-61%) in the Bronx and 64% (IQR 55%-72%) in Washington, D.C. Conclusions: In a novel use of site-aggregated surveillance data, baseline data was used to design and evaluate site randomized studies for both HIV test and HIV care sites. Surveillance data have the potential to inform and monitor sitelevel health outcomes in HIV-infected patients

The hybrid spectral problem and Robin boundary conditions

The hybrid spectral problem where the field satisfies Dirichlet conditions (D) on part of the boundary of the relevant domain and Neumann (N) on the remainder is discussed in simple terms. A conjecture for the C_1 coefficient is presented and the conformal determinant on a 2-disc, where the D and N regions are semi-circles, is derived. Comments on higher coefficients are made. A hemisphere hybrid problem is introduced that involves Robin boundary conditions and leads to logarithmic terms in the heat--kernel expansion which are evaluated explicitly.Comment: 24 pages. Typos and a few factors corrected. Minor comments added. Substantial Robin additions. Substantial revisio