Relaxation of spins due to a magnetic field gradient, revisited; Identity of the Redfield and Torrey theories

There is an extensive literature on magnetic gradient induced spin relaxation. Cates, Schaefer and Happer (CSH) in a seminal paper, have solved the problem in the regime where diffusion theory (the Torrey equation is applicable using an expansion of the density matrix in diffusion equation eigenfunctions and angular momentum tensors. McGregor has solved the problem in the same regime using a slightly more general formulation using Redfield theory formulated in terms of the auto-correlation function of the fluctuating field seen by the spins and calculating the correlation functions using the diffusion theory Green's function. The results of both calculations were shown to agree for a special case. In the present work we show that the eigenfunction expansion of the Torrey equation yields the expansion of the Green's function for the diffusion equation thus showing the identity of this approach with that of Redfield theory. The general solution can also be obtained directly from the Torrey equation for the density matrix. Thus the physical content of the Redfield and Torrey approaches are identical. We then introduce a more general expression for the position autocorrelation function of particles moving in a closed cell, extending the range of applicability of the theory.Comment: 2 figure

Moduli potentials in string compactifications with fluxes: mapping the Discretuum

We find de Sitter and flat space solutions with all moduli stabilized in four dimensional supergravity theories derived from the heterotic and type II string theories, and explain how all the previously known obstacles to finding such solutions can be removed. Further, we argue that if the compact manifold allows a large enough space of discrete topological choices then it is possible to tune the parameters of the four dimensional supergravity such that a hierarchy is created and the solutions lie in the outer region of moduli space in which the compact volume is large in string units, the string coupling is weak, and string perturbation theory is valid. We show that at least two light chiral superfields are required for this scenario to work, however, one field is sufficient to obtain a minimum with an acceptably small and negative cosmological constant. We discuss cosmological issues of the scenario and the possible role of anthropic considerations in choosing the vacuum of the theory. We conclude that the most likely stable vacuua are in or near the central region of moduli space where string perturbation theory is not strictly valid, and that anthropic considerations cannot help much in choosing a vacuum.Comment: 34 pages, no figure

Fivebranes and 4-manifolds

We describe rules for building 2d theories labeled by 4-manifolds. Using the proposed dictionary between building blocks of 4-manifolds and 2d N=(0,2) theories, we obtain a number of results, which include new 3d N=2 theories T[M_3] associated with rational homology spheres and new results for Vafa-Witten partition functions on 4-manifolds. In particular, we point out that the gluing measure for the latter is precisely the superconformal index of 2d (0,2) vector multiplet and relate the basic building blocks with coset branching functions. We also offer a new look at the fusion of defect lines / walls, and a physical interpretation of the 4d and 3d Kirby calculus as dualities of 2d N=(0,2) theories and 3d N=2 theories, respectivelyComment: 81 pages, 18 figures. v2: misprints corrected, clarifications and references added. v3: additions and corrections about lens space theory, 4-manifold gluing, smooth structure

M-Theory Moduli Space and Cosmology

We conduct a systematic search for a viable string/M-theory cosmology, focusing on cosmologies that include an era of slow-roll inflation, after which the moduli are stabilized and the Universe is in a state with an acceptably small cosmological constant. We observe that the duality relations between different cosmological backgrounds of string/M-theory moduli space are greatly simplified, and that this simplification leads to a truncated moduli space within which possible cosmological solutions lie. We review some known challenges to four dimensional models in the "outer", perturbative, region of moduli space, and use duality relations to extend them to models of all of the (compactified) perturbative string theories and 11D supergravity, including brane world models. We conclude that cosmologies restricted to the outer region are not viable, and that the most likely region of moduli space in which to find realistic cosmology is the "central", non-perturbative region, with coupling and compact volume both of order unity, in string units.Comment: 42 pages, 3 figure

Duality without Supersymmetry: The Case of the SO(16)xSO(16) String

We extend strong/weak coupling duality to string theories without spacetime supersymmetry, and focus on the case of the unique ten-dimensional, nonsupersymmetric, tachyon-free $SO(16)\times SO(16)$ heterotic string. We construct a tachyon-free heterotic string model that interpolates smoothly between this string and the ten-dimensional supersymmetric $SO(32)$ heterotic string, and we construct a dual for this interpolating model. We find that the perturbative massless states of our dual theories precisely match within a certain range of the interpolation. Further evidence for this proposed duality comes from a calculation of the one-loop cosmological constant in both theories, as well as the presence of a soliton in the dual theory. This is therefore the first known duality relation between nonsupersymmetric tachyon-free string theories. Using this duality, we then investigate the perturbative and nonperturbative stability of the $SO(16)\times SO(16)$ string, and present a conjecture concerning its ultimate fate.Comment: 15 pages, LaTeX, 3 figure

Gaugino Condensation in M-theory on S^1/Z_2

In the low energy limit of for M-theory on S^1/Z_2, we calculate the gaugino condensate potential in four dimensions using the background solutions due to Horava. We show that this potential is free of delta-function singularities and has the same form as the potential in the weakly coupled heterotic string. A general flux quantization rule for the three-form field of M-theory on S^1/Z_2 is given and checked in certain limiting cases. This rule is used to fix the free parameter in the potential originating from a zero mode of the form field. Finally, we calculate soft supersymmetry breaking terms. We find that corrections to the Kahler potential and the gauge kinetic function, which can be large in the strongly coupled region, contribute significantly to certain soft terms. In particular, for supersymmetry breaking in the T-modulus direction, the small values of gaugino masses and trilinear couplings that occur in the weakly coupled, large radius regime are enhanced to order m_3/2 in M-theory. The scalar soft masses remain small even, in the strong coupling M-theory limit.Comment: 20 pages, LATE

Moduli Stabilisation in Heterotic Models with Standard Embedding

In this note we analyse the issue of moduli stabilisation in 4d models obtained from heterotic string compactifications on manifolds with SU(3) structure with standard embedding. In order to deal with tractable models we first integrate out the massive fields. We argue that one can not only integrate out the moduli fields, but along the way one has to truncate also the corresponding matter fields. We show that the effective models obtained in this way do not have satisfactory solutions. We also look for stabilised vacua which take into account the presence of the matter fields. We argue that this also fails due to a no-go theorem for Minkowski vacua in the moduli sector which we prove in the end. The main ingredient for this no-go theorem is the constraint on the fluxes which comes from the Bianchi identity.Comment: 20 pages, LaTeX; references adde

Topological Masses From Broken Supersymmetry

We develop a formalism for computing one-loop gravitational corrections to the effective action of D-branes. In particular, we study bulk to brane mediation of supersymmetry breaking in models where supersymmetry is broken at the tree-level in the closed string sector (bulk) by Scherk-Schwarz boundary conditions, while it is realized on a collection of D-branes in a linear or non-linear way. We compute the gravitational corrections to the fermion masses $m_{1/2}$ (gauginos or goldstino) induced from the exchange of closed strings, which are non-vanishing for world-sheets with Euler characteristic -1 (``genus 3/2'') due to a string diagram with one handle and one hole. We show that the corrections have a topological origin and that in general, for a small gravitino mass, the induced mass behaves as $m_{1/2}\propto g^4 m_{3/2}$, with $g$ the gauge coupling. In generic orbifold compactifications however, this leading term vanishes as a consequence of cancellations caused by discrete symmetries, and the remainder is exponentially suppressed by a factor of $\exp(-1/\alpha'm^2_{3/2})$.Comment: 33 pages, 5 figures. v2 is the final Nuclear Physics B version including an additional reference and some minor correction