The heterotic string is a soliton

It is shown that the Type IIA superstring compactified on K3 has a smooth string soliton with the same zero mode structure as the heterotic string compactified on a four-torus, thus providing new evidence for a conjectured exact duality between the two six-dimensional string theories. The chiral worldsheet bosons arise as zero modes of Ramond-Ramond fields of the IIA string theory and live on a signature (20,4) even, self-dual lattice. Stable, finite loops of soliton string provide the charged Ramond-Ramond states necessary for enhanced gauge symmetries at degeneration points of the K3 surface. It is also shown that Type IIB strings toroidally compactified to six dimensions have a multiplet of string solutions with Type II worldsheets.     

Supersymmetric standard model from the heterotic string

We present a [FORMULA: SEE TEXT] orbifold compactification of the E8xE8 heterotic string which leads to the (supersymmetric) standard model gauge group and matter content. The quarks and leptons appear as three 16-plets of SO(10), whereas the Higgs fields do not form complete SO(10) multiplets. The model has large vacuum degeneracy. For generic vacua, no exotic states appear at low energies and the model is consistent with gauge coupling unification. The top quark Yukawa coupling arises from gauge interactions and is of the order of the gauge couplings, whereas the other Yukawa couplings are suppressed.     

Non-supersymmetric gauge theories from D-branes in type 0 string theory

We construct non-supersymmetric four-dimensional gauge theories arising as effective theories of D-branes placed on various singularities in Type 0B string theory. We mostly focus on models which are conformal in the large-N limit and present both examples appearing on self-dual D3-branes on orbifold singularities and examples including orientifold planes. Moreover, we derive type 0 Hanany-Witten setups with NS 5-branes intersected by D-branes and the corresponding rules for determining the massless spectra. Finally, we discuss possible duality symmetries (Seiberg duality) for non-supersymmetric gauge theories within this framework.     

Interactions of strings and D-branes from M theory

We discuss the relation between M theory and type II string theories. We show that, assuming “natural” interactions between membranes and fivebranes in M theory, the known interactions between strings and D-branes in type II string theories arise in appropriate limits. Our discussion of the interactions is purely at the classical level. We remark on issues associated with the M theory approach to enhanced gauge symmetries, which deserve further investigation.     

Exotic Tensor Gauge Theory and Duality

 Gauge fields in exotic representations of the Lorentz group in D dimensions – i.e. ones which are tensors of mixed symmetry corresponding to Young tableaux with arbitrary numbers of rows and columns – naturally arise through massive string modes and in dualising gravity and other theories in higher dimensions. We generalise the formalism of differential forms to allow the discussion of arbitrary gauge fields. We present the gauge symmetries, field strengths, field equations and actions for the free theory, and construct the various dual theories. In particular, we discuss linearised gravity in arbitrary dimensions, and its two dual forms. Received: 9 September 2002 / Accepted: 22 October 2002 Published online: 21 February 2003 Communicated by A. Connes     

Sequestering by global symmetries in Calabi-Yau string models

We study the possibility of realizing an effective sequestering between visible and hidden sectors in generic heterotic string models, generalizing previous work on orbifold constructions to smooth Calabi-Yau compactifications. In these theories, genuine sequestering is spoiled by interactions mixing chiral multiplets of the two sectors in the effective Kähler potential. These effective interactions however have a specific current-current-like structure and can be interpreted from an M-theory viewpoint as coming from the exchange of heavy vector multiplets. One may then attempt to inhibit the emergence of generic soft scalar masses in the visible sector by postulating a suitable global symmetry in the dynamics of the hidden sector. This mechanism is however not straightforward to implement, because the structure of the effective contact terms and the possible global symmetries is a priori model-dependent. To assess whether there is any robust and generic option, we study the full dependence of the Kähler potential on the moduli and the matter fields. This is well known for orbifold models, where it always leads to a symmetric scalar manifold, but much less understood for Calabi-Yau models, where it generically leads to a non-symmetric scalar manifold. We then examine the possibility of an effective sequestering by global symmetries, and argue that whereas for orbifold models this can be put at work rather naturally, for Calabi-Yau models it can only be implemented in rather peculiar circumstances.     

Gauge couplings in four-dimensional type I string orbifolds

We compute threshold effects to gauge couplings in four-dimensional _N orientifold models of type I strings with GN = 2 and GN = 1 supersymmetry, and study their dependence on the geometric moduli. We also compute the tree-level (disk) couplings of the open sector gauge fields to the twisted closed string moduli of the orbifold in various models and study their effects and that of the one-loop threshold corrections on gauge coupling unification. We interpret the results from the (supergravity) effective theory point of view and comment on the conjectured heterotic-type I duality.     

Power-like threshold corrections to gauge unification in extra dimensions

One of the much-debated novel features of theories with extra dimensions is the presence of power-like loop corrections to gauge coupling unification, which have the potential of allowing a significant reduction of the unification scale. A recognized problem of such scenarios is the UV sensitivity of the above power corrections. We consider situations where the grand unified group is broken by the vacuum expectation value of a bulk field and find that, because of the softness of this extra-dimensional symmetry-breaking mechanism, power-like threshold corrections are calculable and generic in many of the most relevant settings. While the precision is limited by the presence of higher-dimension bulk operators, the most dangerous of these operators are naturally forbidden by symmetries of the bulk theory. Particularly interesting and constrained scenarios arise in the context of higher-dimensional supersymmetry. Our phenomenological exploration of SU(5) models in 5d, linked in particular with more recently discussed orbifold GUT models, shows promising results.     

Heterotic and Type I string dynamics from eleven dimensions

We propose that the ten-dimensional E₈ × E₈ heterotic string is related to an eleven-dimensional theory on the orbifold in the same way that the Type IIA string in ten dimensions is related to . This in particular determines the strong coupling behavior of the ten-dimensional E₈ × E₈ theory. It also leads to a plausible scenario whereby duality between SO(32) heterotic and Type I superstrings follows from the classical symmetries of the eleven-dimensional world, just as the duality of the ten-dimensional Type IIB theory follows from eleven-dimensional diffeomorphism invariance.     

Gauge threshold corrections in intersecting brane world models

We calculate the one‐loop corrections to gauge couplings in N = 1 supersymmetric brane world models, which are realized in an type IIA orbifold/orientifold background with several stacks of D6 branes wrapped on 3‐cycles with non‐vanishing intersections. Contributions arise from both N = 1 and N = 2 open string subsectors. In contrast to what is known from ordinary orbifold theories, N = 1 subsectors do give rise to moduli‐dependent one‐loop corrections.     

Field theory in two-time physics with N=1 supersymmetry

We construct N=1 supersymmetric (SUSY) field theory in 4+2 dimensions compatible with the theoretical framework of two-time (2T) physics and its gauge symmetries. The fields are arranged into 4+2 dimensional chiral and vector supermultiplets, and their interactions are uniquely fixed by SUSY and 2T physics gauge symmetries. In a particular gauge the 4+2 theory reduces to ordinary supersymmetric field theory in 3+1 dimensions without any Kaluza-Klein remnants, but with some additional constraints in 3+1 dimensions of interesting phenomenological relevance. This construction is another significant step in the development of 2T physics as a structure that stands above 1T physics.     

Momentum lattice for CHL string

We propose some analogue of the Narain lattice for CHL string. The symmetries of this lattice are the symmetries of the perturbative spectrum. We explain in this language the known results about the possible gauge groups in compactified theory. For the four-dimensional theory, we explicitly describe the action of S-duality on the background fields. We show that the moduli spaces of the six-, seven- and eight-dimensional compactifications coincide with the moduli spaces of the conjectured type IIA, M-theory and F-theory duals. We classify the rational components of the boundary of the moduli space in seven, eight and nine dimensions.     

Meeting the constraint of neutrino—Higgsino mixing in gravity unified theories

In gravity unified theories all operators that are consistent with the local gauge and discrete symmetries are expected to arise in the effective low-energy theory. Given the absence of multiplets like 126 of SO(10) in string models, and assuming that B - L is violated spontaneously to generate light neutrino masses via a seesaw mechanism, it is observed that string theory solutions generically face the problem of producing an excessive mixing mass at the GUT scale, which is some nineteen orders of magnitude larger than the experimental bound of 1 MeV. The suppression of mixing, like proton longevity, thus provides one of the most severe constraints on the validity of any string theory solution. We examine this problem in a class of superstring derived models. We find a family of solutions within this class for which the symmetries of the models and an allowed pattern of VEVs, surprisingly, succeed in adequately suppressing the neutrino-Higgsino mixing terms. At the same time they produce the terms required to generate small neutrino masses via a seesaw mechanism.     

On the low energy spectra of the non-supersymmetric heterotic string theories

The ten dimensional string theories as well as eleven dimensional supergravity are conjectured to arise as limits of a more basic theory, traditionally dubbed M-theory. This notion is confined to the ten dimensional supersymmetric theories. String theory, however, also contains ten dimensional non-supersymmetric theories that have not been incorporated into this picture. In this note we explore the possibility of generating the low energy spectra of various non-supersymmetric heterotic string vacua from the Horava–Witten model. We argue that this can be achieved by imposing on the Horava–Witten model an invariance with respect to some extra operators which identify the orbifold fixed planes in a non-trivial way, and we demonstrate it for the E₈ and SO(16)×SO(16) heterotic string vacua in ten dimensions.     

Towards low energy physics from the heterotic string

We investigate orbifold compactifications of the heterotic string, addressing in detail their construction, classification and phenomenological potential. We present a strategy to search for models resembling the minimal supersymmetric extension of the standard model (MSSM) in ℤ₆‐II orbifold compactifications. We find several MSSM candidates with the gauge group and the exact spectrum of the MSSM, and supersymmetric vacua below the compactification scale. They also exhibit the following realistic features: R‐parity, seesaw suppressed neutrino masses, and intermediate scale of supersymmetry breakdown. In addition, we find that similar models also exist in other ℤ_N orbifolds and in the SO(32) heterotic theory.     

Superstring on pp-wave orbifold from large-N quiver gauge theory

We extend the proposal of Berenstein, Maldacena and Nastase to the Type IIB superstring propagating on a pp-wave over the R ⁴/Z _k orbifold. We show that first-quantized free string theory is described correctly by the large-N, fixed gauge coupling limit of [U(N)] ^k quiver gauge theory. We propose a precise map between gauge theory operators and string states for both untwisted and twisted sectors. We also compute leading-order perturbative correction to the anomalous dimensions of these operators. The result is in agreement with the value deduced from the string energy spectrum, thus substantiating our proposed operator-state map. Received: 14 March 2002 / Published online: 5 July 2002     

An Interacting Gauge Field Theoretic Model for Hodge Theory: Basic Canonical Brackets

We derive the basic canonical brackets amongst the creation and annihilation operators for a two （1 ＋ 1）- dimensional （2D） gauge field theoretic model of an interacting Hodge theory where a U（1） gauge field （Aμ） is coupled with the fermionic Dirac fields （ψ and ψ）. In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries （and the concept of their generators） that are present in the theory. We do not use the definition of the canonical conjugate momenta （corresponding to the basic fields of the theory） anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries （and corresponding generators） provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level.     

One-loop Effective Potential in Higher-dimensional Yang-Mills Theory

We study the effective action in Euclidean Yang-Mills theory with a compact simple gauge group in one-loop approximation assuming a covariantly constant gauge field strength as a background. For groups of higher rank and spacetimes of higher dimensions such field configurations have many independent color components taking values in Cartan subalgebra and many “magnetic fields” in each color component. In our previous investigation it was shown that such background is stable in dimensions higher than four provided the amplitudes of “magnetic fields” do not differ much from each other. In the present paper we exactly calculate the relevant zeta-functions in the case of equal amplitudes of “magnetic fields”. For two “magnetic fields” with equal amplitudes the behavior of the effective action is studied in detail. It is shown that in dimensions d = 4,5,6,7 (8), the perturbative vacuum is metastable, i.e., it is stable in perturbation theory but the effective action is not bounded from below, whereas in dimensions d = 9,10,11 (8) the perturbative vacuum is absolutely stable. In dimensions d = 8 (8) the perturbative vacuum is stable for small values of the coupling constant but becomes unstable for large coupling constant leading to the formation of a non-perturbative stable vacuum with nonvanishing “magnetic fields”. The critical value of the coupling constant and the amplitudes of the vacuum “magnetic fields” are evaluated exactly. PACS numbers: 11.10Kk, 11.15Tk, 11.15.-q, 12.38Aw, 12.38Lg     

Linear bosonic quantum field theories arising from causal variational principles

We describe discrete symmetries of two-dimensional Yang–Mills theory with gauge group G associated with outer automorphisms of G, and their corresponding defects. We show that the gauge theory partition function with defects can be computed as a path integral over the space of twisted G-bundles and calculate it exactly. We argue that its weak-coupling limit computes the symplectic volume of the moduli space of flat twisted G-bundles on a surface. Using the defect network approach to generalised orbifolds, we gauge the discrete symmetry and construct the corresponding orbifold theory, which is again two-dimensional Yang–Mills theory but with gauge group given by an extension of G by outer automorphisms. With the help of the orbifold completion of the topological defect bicategory of two-dimensional Yang–Mills theory, we describe the reverse orbifold using a Wilson line defect for the discrete gauge symmetry. We present our results using two complementary approaches: in the lattice regularisation of the path integral, and in the functorial approach to area-dependent quantum field theories with defects via regularised Frobenius algebras.

     

Flat directions,string compactification and three generation models

We show how identification of absolutely flat directions allows the construction of a new class of compactified string theories with reduced gauge symmetry that may or may not be continuously connected to the original theory. We use this technique to construct a class of three generation models with just the Standard Model gauge group after compactification. We discuss the low-energy symmetries necessary for a phenomenologically viable low-energy model and construct an example in which these symmetries are identified with string symmetries which remain unbroken down to the supersymmetry breaking scale. Remarkably the same symmetry responsible for stabilising the nucleon is also responsible for ensuring one and only one pair of Higgs doublets is kept light. We show how the string symmetries also lead to textures in the quark and lepton mass matrices which can explain the hierarchy of fermion masses and mixing angles.