John March-Russell

Kinetic mixing and the supersymmetric gauge hierarchy

The most general Lagrangian for a model with two U(1) gauge symmetries contains a renormalizable operator which mixes their gauge kinetic terms. Such kinetic mixing can be generated at arbitrarily high scales but will not be suppressed by large masses. In models whose supersymmetry (SUSY)-breaking hidden sectors contain U(1) gauge factors, we show that such terms will generically arise and communicate SUSY breaking to the visible sector through mixing with hypercharge. In the context of the usual supergravity- or gauge-mediated communication scenarios with D-terms of order the fundamental scale of SUSY breaking, this effect can destabilize the gauge hierarchy. Even in models for which kinetic mixing is suppressed or the D-terms are arranged to be small, this effect is a potentially large correction to the soft scalar masses and therefore introduces a new measurable low-energy parameter. We calculate the size of kinetic mixing both in field theory and in string theory, and argue that appreciable kinetic mixing is a generic feature of string models. We conclude that the possibility of kinetic mixing effects cannot be ignored in model building and in phenomenological studies of the low-energy SUSY spectra.

Planck-scale physics and the Peccei-Quinn mechanism

Global-symmetry violating higher-dimension operators, expected to be induced by Planck-scale physics, in general drastically alter the properties of the axion field associated with the Peccei-Quinn solution to the strong-CP problem, and render this solution unnatural. The particle physics and cosmology associated with other global symmetries can also be significantly changed.

ENHANCED BARYON NUMBER VIOLATION DUE TO COSMIC STRINGS

Abstract When quarks and leptons propagate in the background of a grand unified cosmic string, various baryon number violating processes can occur. We argue that, because of the long-range pure gauge field that surrounds the string, the cross sections for these processes are generically enhanced by large factors over the naive, geometric, cross section. We explicitly calculate the cross section for quark to lepton transitions in a simplified model and find that it is enhanced by a factor of up to ( Λ / M proton ) 2 where Λ is the grand unification scale. In an appendix we discuss the possible boundary conditions for the fermionic wave functions, and calculate the correct choice of boundary condition for our model system.

Building models of gauge-mediated supersymmetry breaking without a messenger sector

Abstract We propose a general scheme for constructing models in which the Standard Model (SM) gauge interactions are the mediators of supersymmetry breaking to the fields in the supersymmetric SM, but where the SM gauge groups couple directly to the sector which breaks supersymmetry dynamically. Despite the direct coupling, the models preserve perturbative unification of the SM gauge coupling constants. Furthermore, the supergravity contributions to the squark and slepton masses can be naturally small, typically being much less than 1% of the gauge-mediated (GM) contributions. Both of these goals can be achieved without need of a fine-tuning or a very small coupling constant. This scheme requires run-away directions at the renormalizable level which are only lifted by non-renormalizable terms in the superpotential. To study the proposed scheme in practice, we develop a modified class of models based on SU ( N ) × SU ( N − 1) which allows us to gauge an SU ( N − 2) global symmetry. However, we point out a new problem which can exist in models where the dynamical supersymmetry breaking sector and the ordinary sector are directly coupled - the two-loop renormalization group has contributions which can induce negative (mass) 2 for the squarks and sleptons. We clarify the origin of the problem and argue that it is likely to be surmountable. We give a recipe for a successful model.

Discrete quantum hair on black holes and the non-abelian Aharonov-Bohm effect

In an abelian Higgs model where U(1) is broken to Zp by a condensate of charge pe, the U(1) charge QV in a finite volume V is an observable, but charge is screened, so 〈 QV 〉 falls exponentially to zero as V → ∞. It is demonstrated that the Zp charge, QV modulo pe, can be cast as a surface integral by evaluating exp(2πiQVpe) in states containing a shell of unbroken vacuum around the volume, and its value is unaffected by the presence of the condensate inside the shell. Thus in these states QV modulo pe is not screened. This shows that black holes can indeed have Zp hair. The extension to a non-abelian discrete gauge charge is discussed, and the detection of this charge by its non-abelian Aharonov-Bohm interaction with cosmic strings is described.

Zero modes of non-abelian vortices

We investigate the bosonic zero modes of cosmic strings formed in the breaking of a gauge group G → H, and find exact charge-carrying zero mode solutions. For the case of G = U(1) × U(1) we find that it is necessary to modify Wittens superconducting zero mode ansatz. In the case of non-abelian G, zero modes are generically present. Further, in the presence of a non-abelian string the embedding of H in G is angle dependent, with only a subgroup H being globally single valued. This subgroup is determined by the Wilson loop integral around the string, and depends on detailed dynamics. We find that gauge bosons associated with multivalued generators Aharonov-Bohm scatter off the string. The Alice string (H = O(2), H = Z2) has novel electrodynamics: it attracts charges, scatters the SO(2) “photon”, and a two-string system has zero modes with unlocalizable (“Cheshire”) charge. We extend this analysis to generalized Alice strings and end by considering the bosonic zero modes of domain walls.

Quantum field theory of non-abelian strings and vortices

We develop an operator formalism for investigating the properties of non-abelian cosmic strings (and vortices) in quantum field theory. Operators are constructed that introduce classical string sources and that create dynamical string loops. The operator construction in lattice gauge theory is explicitly described, and correlation functions are computed in the strong-coupling and weak-coupling limits. These correlation functions are used to study the long-range interactions of non-abelian strings, taking account of charge-screening effects due to virtual particles. Among the phenomena investigated are the Aharonov-Bohm interactions of strings with charged particles, holonomy interactions between string loops, string entanglement, the transfer of “Cheshire charge” to a string loop, and domain-wall decay via spontaneous string nucleation. We also anayze the Aharonov-Bohm interactions of magnetic monopoles with electric flux tubes in a confining gauge theory. We propose that the Aharonov-Bohm effect can be invoked to distinguish among various phases of a non-abelian gauge theory coupled to matter.

Baryons from quarks in the 1N expansion

We present a new formalism for treating baryons in the 1N expansion, where N is the number of QCD colors, based on an analysis of quark-level diagrams. This method allows us to derive known results on the large-N limit in a very efficient and transparent manner: we show that there are an infinite number of degenerate baryon states in the large-N limit, and that forward matrix elements of quark bilinear operators satisfy the static quark-model relations. We also derive new results: we enumerate the corrections to the large-N relations to all orders in 1N, and write an explicit effective lagrangian for baryon chiral perturbation theory which respects chiral symmetry to all orders in 1N. These results give a simple algorithm to apply the 1N expansion for baryons at N = 3. Finally, we compare our results for the corrections to the large -N relations to what is expected from a chiral constituent quark model.

String unification, higher-level gauge symmetries, and exotic hypercharge normalizations

Abstract We explore the extent to which string theories with higher-level gauge symmetries and nonstandard hypercharge normalizations can reconcile the discrepancy between the string unification scale and the GUT scale extrapolated from the Minimal Supersymmetric Standard Model (MSSM). We determine the phenomenologically allowed regions of (ky, k2, k3) parameter space, and investigate the proposal that there might exist string models with exotic hypercharge normalizations ky which are less than their usual value k y = 5 3 . For a broad class of heterotic string models (encompassing most realistic string models which have been constructed), we prove that k y ⩾ 5 3 . Beyond this class, however, we show that there exist consistent MSSM embeddings which lead to k y 5 3 . We also consider the constraints imposed on by demanding charge integrality of all unconfined string states, and show that only a limited set of hypercolor confining groups and corresponding values of ky are possible.

Realizing higher-level gauge symmetries in string theory: new embeddings for string GUTs

Abstract We consider the methods by which higher-level and non-simply laced gauge symmetries can be realized in free-field heterotic string theory. We show that all such realizations have a common underlying feature, namely a dimensional truncation of the charge lattice, and we identify such dimensional truncations with certain irregular embeddings of higher-level and non-simply laced gauge groups within level-one simply laced gauge groups. This identification allows us to formulate a direct mapping between a given subgroup embedding, and the sorts of GSO constraints that are necessary in order to realize the embedding in string theory. This also allows us to determine a number of useful constraints that generally affect string GUT model-building. For example, most string GUT realizations of higher-level gauge symmetries G k employ the so-called diagonal embeddings G k ∉ G × G × … × G . We find that there exist interesting alternative embeddings by which such groups can be realized at higher levels, and we derive a complete list of all possibilities for the GUT groups SU (5), SU (6), SO (10), and E 6 at levels k = 2,3,4 (and in some cases up to k = 7). We find that these new embeddings are always more efficient and require less central charge than the diagonal embeddings which have traditionally been employed. As a by-product, we also prove that it is impossible to realize SO (10) at levels k > 4 in string theory. This implies, in particular, that free-field heterotic string models can never give a massless 126 representation of SO (10).