Robustness and Predictivity of 4 TeV Unification

The stability of the predictions of two of the standard model parameters, $\alpha_3(M_Z)$ and $\sin^2 \theta(M_Z)$, in a $M_U \sim 4$ TeV unification model is examined. It is concluded that varying the unification scale between $M_U \simeq 2.5$ TeV and $M_U \simeq 5$ TeV leaves robust all predictions within reasonable bounds. Choosing $M_U = 3.8 \pm 0.4$ TeV gives, at lowest order, accurate predictions at $M_Z$. Flavor-changing effects and deviations from precision electroweak data are discussed

Reexamination of relaxation of spins due to a magnetic field gradient: Identity of the Redfield and Torrey theories

There is an extensive literature on magnetic-gradient-induced spin relaxation. Cates, Schaefer, and Happer, in a seminal publication, 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 the Redfield theory formulated in terms of the autocorrelation 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 the 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

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

The Ursinus Weekly, February 18, 1957

Visiting group to complete U.C. evaluation this week • Twenty students enter at mid-year • Men\u27s council hears suggestions • Curtain Club to present The Valiant on Feb. 26 • W.F. Speilman, member of UC maintenance staff, dies • Chest drive dates released • Y association to hear refugees • Senate decides on WSGA revisions • Frosh women\u27s representatives chosen; To be installed on Color Day, Thursday • St. John Terrell addresses Forum on drama history • Peirce - Pauli engagement • Dave Burger made king of annual Lorelei, Fri., Feb. 15 • Selective Service rules published by administration • Snyder receives Ph.D. degree Feb. 9 • S.R.C. discusses mental health • Two UC women attend confab on religious work • Chess Club plays F&M • Editorial: Word of welcome and some comments on evaluation • May Day • Brotherhood Week and the work of the National Conference of Christians and Jews • IRC to hear talk tonight on U.S. and Phillipines • Age of service • Cagers lose to Fords in overtime; Lose to Garnet five Saturday, 84-64 • Ursinus mermaids defeat Drexel Wed. • Belles register two net shutouts • William Yost resigns from court post • Padula stopped as matmen score win over E\u27town, Sat. • Chi Alpha hears Baker, sponsors weekly talks • Newman Club to hear discussion on J.H. Newman • Y heads discuss activities, plans at retreat, Sat. • Pre-med society hears Mercurio; Plans dinner • Fourteen go on mid-year trip to Washington, D.C. • Reed and Barton contest to run through Feb., Mar.https://digitalcommons.ursinus.edu/weekly/1421/thumbnail.jp

Real Special Geometry

We give a coordinate-free description of real manifolds occurring in certain four dimensional supergravity theories with antisymmetric tensor fields. The relevance of the linear multiplets in the compactification of string and five-brane theories is also discussed.Comment: 10 pgs (TeX with Harvmac), CERN-TH.7211/94, UCLA/94/TEP/14, POLFIS-TH.01/9

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

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

New Sum Rules from Low Energy Compton Scattering on Arbitrary Spin Target

We derive two sum rules by studying the low energy Compton scattering on a target of arbitrary (nonzero) spin j. In the first sum rule, we consider the possibility that the intermediate state in the scattering can have spin |j \pm 1| and the same mass as the target. The second sum rule applies if the theory at hand possesses intermediate narrow resonances with masses different from the mass of the scatterer. These sum rules are generalizations of the Gerasimov-Drell-Hearn-Weinberg sum rule. Along with the requirement of tree level unitarity, they relate different low energy couplings in the theory. Using these sum rules, we show that in certain cases the gyromagnetic ratio can differ from the "natural" value g=2, even at tree level, without spoiling perturbative unitarity. These sum rules can be used as constraints applicable to all supergravity and higher-spin theories that contain particles charged under some U(1) gauge field. In particular, applied to four dimensional N=8 supergravity in a spontaneously broken phase, these sum rules suggest that for the theory to have a good ultraviolet behavior, additional massive states need to be present, such as those coming from the embedding of the N=8 supergravity in type II superstring theory. We also discuss the possible implications of the sum rules for QCD in the large-N_c limit.Comment: 18 pages, v2: discussion on black hole contribution is included, references added; v3: extended discussion in introduction, version to appear in JHE

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