1,371 research outputs found
Zero modes and conformal anomaly in liouville vortices
No full textThe partition function of a two-dimensional Abelian gauge model reproducing magnetic vortices is discussed in the harmonic approximation. Classical solutions exhibit conformal invariance, that is broken by statistical fluctuations, apart from an exceptional case. The corresponding “anomaly” has been evaluated. Zero-modes of the thermal fluctuation operator have been carefully discussed
ET sensitivity to the anisotropic Stochastic Gravitational Wave Background
No full textWe study the sensitivity of a pair of Einstein Telescopes (ET) (hypothetically located at the two sites currently under consideration for ET) to the anisotropies of the Stochastic Gravitational Wave Background (SGWB). We focus on the l =0,2,4 multipoles of an expansion of the SGWB in spherical harmonics, since the sensitivity to other multipoles is suppressed due to the fact that this pair of detector operates in a regime for which the product between the observed frequency and the distance between the two sites is much smaller than one. In this regime, the interferometer overlap functions for the anisotropic signal acquire very simple analytic expressions. These expressions can also be applied to any other pairs of interferometers (each one of arbitrary opening angle between its two arms) operating in this regime. Once the measurements at the vertices of the two sites are optimally combined, the sensitivity to the multipoles of the SGWB depends only on the latitude of the two sites, on the difference of their longitude, but not on the orientation of their arms
Some remarks on L¹ embeddings in the subelliptic setting
No full textIn this paper we establish an optimal Lorentz estimate for the Riesz potential in the L1 regime in the setting of a stratified group G: Let Q >= 2 be the homogeneous dimension of G and Ia denote the Riesz potential of order a on G. Then, for every alpha is an element of (0, Q), there exists a constant C = C(alpha, Q) > 0 such that parallel to I(alpha)f parallel to L-Q/(Q-alpha),L-1(G) <= C parallel to XI(1)f parallel to(L1(G)) (0.1)
for all f is an element of C-c(infinity) (G) such that XI(1)f is an element of L-1(G), where X denotes the horizontal gradient
Chiral gravity as a covariant formulation of massive gravity
No full textWe present a covariant nonlinear completion of the Fierz-Pauli (FP) mass term for the graviton. The starting observation is that the FP mass is immediately obtained by expanding the cosmological constant term, i.e. the determinant of the vielbein, around Minkowski space to second order in the vielbein perturbations. Since this is an unstable expansion in the standard case, we consider an extended theory of gravity which describes two vielbeins that give rise to chiral spin-connections (consequently, fermions of a definite chirality only couple to one of the gravitational sectors). As for Einstein gravity with a cosmological constant, a single fine-tuning is needed to recover a Minkowski background; the two sectors then differ only by a constant conformal factor. The spectrum of this theory consists of a massless and a massive graviton, with FP mass term. The theory possesses interesting limits in which only the massive graviton is coupled to matter at the linearized level
COSMOLOGICAL PERTURBATIONS AND SHORT DISTANCE PHYSICS FROM NONCOMMUTATIVE GEOMETRY
No full text[HEP-TH 0203099] Spires Archive "Well known paper" (50+ citations
Sobolev algebras on nonunimodular Lie groups
No full textLet G be a noncompact connected Lie group and. be the right Haar measure of G. Let X = {X1,..., Xq} be a family of left invariant vector fields which satisfy Hormander's condition, and let Delta = -Sigma(q)(i=1) X-i(2) be the corresponding subLaplacian. For 1 = p < 8 and a = 0 we define the Sobolev space
L-alpha(p) (G) = {f is an element of L-p (.) : a/2 f. L-p (.)},
endowed with the norm
vertical bar vertical bar f vertical bar vertical bar a, p = vertical bar vertical bar f vertical bar vertical bar(p) + vertical bar vertical bar Delta(a/2) f vertical bar vertical bar(p), where we denote by f p the norm of f in L-p(.). In this paper we show that for all a = 0 and p. (1,8), the space L 8 n L-p a (G) is an algebra under pointwise product, that is, there exists a positive constant Ca, p such that for all f, g. L 8n L-p a (G), f g. L 8n L-p a (G) and
vertical bar vertical bar fg vertical bar vertical bar a,p <= Ca,p (vertical bar vertical bar f vertical bar vertical bar a,p vertical bar vertical bar g vertical bar vertical bar(infinity) + vertical bar vertical bar f vertical bar vertical bar(infinity) vertical bar vertical bar g vertical bar vertical bar a, p).
Such estimates were proved by Coulhon, Russ and Tardivel-Nachef in the case when G is unimodular. We shalL(p)rove it on Lie groups, thus extending their result to the nonunimodular case. In order to prove our main result, we need to study the boundedness of local Riesz transforms Rc J = XJ (cI + ) -m/2, where c > 0, XJ = X j1... X jm and j . {1,..., q} for = 1,..., m. We show that if c is sufficiently large, the Riesz transform Rc J is bounded on L-p(rho) for every p is an element of (1, infinity), and prove also appropriate endpoint results involving Hardy and BMO spaces
Probing the galactic and extragalactic gravitational wave backgrounds with space-based interferometers
No full textWe employ the formalism developed in [1] and [2] to study the prospect of detecting an anisotropic Stochastic Gravitational Wave Background (SGWB) with the Laser Interferometer Space Antenna (LISA) alone, and combined with the proposed space-based interferometer Taiji. Previous analyses have been performed in the frequency domain only. Here, we study the detectability of the individual coefficients of the expansion of the SGWB in spherical harmonics, by taking into account the specific motion of the satellites. This requires the use of time-dependent response functions, which we include in our analysis to obtain an optimal estimate of the anisotropic signal. We focus on two applications. Firstly, the reconstruction of the anisotropic galactic signal without assuming any prior knowledge of its spatial distribution. We find that both LISA and LISA with Taiji cannot put tight constraints on the harmonic coefficients for realistic models of the galactic SGWB. We then focus on the discrimination between a galactic signal of known morphology but unknown overall amplitude and an isotropic extragalactic SGWB component of astrophysical origin. In this case, we find that the two surveys can confirm, at a confidence level ≳ 3σ, the existence of both the galactic and extragalactic background if both have amplitudes as predicted in standard models. We also find that, in the LISA-only case, the analysis in the frequency domain (under the assumption of a time average of data taken homogeneously across the year) provides a nearly identical determination of the two amplitudes as compared to the optimal analysis
New results on the Bergman kernel of the worm domain in complex space
No full textWe study the Bergman kernel and projection on the worm domains for β > π. We calculate the kernels explicitly, up to an error term that can be controlled. Denote by P the Bergman projection on Dβ and by P′ the one on D′β. We show that is bounded when 1 < p < ∞, while if and only if 2/(1 + vβ) < p < 2/(1 - vβ), where vβ = π/(2β - π). Along the way, we give a new proof of the failure of Condition R on these worms. Finally, we are able to show that the singularities of the Bergman kernel on the boundary are not contained in the boundary diagonal
- …
