String Theory and the Velo–Zwanziger problem

We examine the behavior of the leading Regge trajectory of the open bosonic string in a uniform electromagnetic background and present a consistent set of Fierz–Pauli conditions for these symmetric tensors that generalizes the Argyres–Nappi spin-2 result. These equations indicate that String Theory does bypass the Velo–Zwanziger problem, i.e. the loss of causality experienced by a massive high-spin field minimally coupled to electromagnetism. Moreover, we provide some evidence that only the first Regge trajectory can be described in isolation and show that the open-string spectrum is free of ghosts in weak constant backgrounds. Finally, we comment on the roles of the critical dimension and of the gyromagnetic ratio.     

Time-dependent supergravity solutions in null dilaton background

A class of time dependent pp-waves with NS–NS flux in type IIA string theory is considered. The background preserves 1/4 supersymmetry and may provide a toy model of Big Bang cosmology with nontrivial flux. At the Big Bang singularity in early past, the string theory is strongly coupled and matrix string model can be used to describe the dynamics. We also construct some time dependent supergravity solutions for D-branes and analyze their supersymmetry properties.     

High energy string–brane scattering for massive states

String–brane interactions provide an ideal framework to study the dynamics of the massive states of the string spectrum in a non-trivial background. We present here an analysis of tree-level amplitudes for processes in which an NS–NS string state from the leading Regge trajectory scatters from a D-brane into another state from the leading Regge trajectory, in general of a different mass, at high energies and small scattering angles. This is done by using world-sheet OPE methods and effective vertex operators. We find that this class of processes has a universal dependence on the energy of the projectile. We then compare the result for these inelastic processes with that which one would obtain from the eikonal operator in a non-trivial test of its ability to describe transitions between different string mass levels. The two are found to be in agreement.     

Non-supersymmetric orientifolds of Gepner models

Starting from a previously collected set of tachyon-free closed strings, we search for N=2$N=2$ minimal model orientifold spectra which contain the standard model and are free of tachyons and tadpoles at lowest order. For each class of tachyon-free closed strings – bulk supersymmetry, automorphism invariants or Klein bottle projection – we do indeed find non-supersymmetric and tachyon free chiral brane configurations that contain the standard model. However, a tadpole-cancelling hidden sector could only be found in the case of bulk supersymmetry. Although about half of the examples we have found make use of branes that break the bulk space–time supersymmetry, the resulting massless open string spectra are nevertheless supersymmetric in all cases. Dropping the requirement that the standard model be contained in the spectrum, we find chiral tachyon and tadpole-free solutions in all three cases, although in the case of bulk supersymmetry all massless spectra are supersymmetric. In the other two cases we find truly non-supersymmetric spectra, but a large fraction of them are nevertheless partly or fully supersymmetric at the massless level.     

Spontaneous supersymmetry breaking induced by vacuum condensates

We propose a novel mechanism of spontaneous supersymmetry breaking which relies upon a ubiquitous feature of Quantum Field Theory, vacuum condensates. Such condensates play a crucial role in many phenomena. Examples include Unruh effect, superconductors, particle mixing, and quantum dissipative systems. We argue that in all these phenomena supersymmetry, when present, is spontaneously broken. Evidence for our conjecture is given for the Wess–Zumino model, that can be considered as an approximation to the supersymmetric extensions of the above mentioned systems. The magnitude of the effect is estimated for a recently proposed experimental setup based on an optical lattice.     

Supersymmetrical dual string theory

It is proved that the physical states of the open-string sector of the ten-dimensional string theory form supersymmetry multiplets. The proof is achieved by first constructing a new formulation of the spectrum generating algebra, and then forming the supersymmetry operator (as well as associated operators) and demonstrating that it transforms as a spinor under Lorentz transformations and has the correct anticommutation relations. The results can be interpreted either in terms of a covariant formulation or in terms of a light-cone gauge formulation. In the former case certain formulas are not completely proved, although they are in the latter. When interpreted in four dimensions (by dimensional reduction) the string theory provides an interacting theory of an infinite number of massive representations of N = 4 supersymmetry involving particles of arbitrarily high spin.     

Non-archimedean string dynamics

Explicit formulas for the N-point tree amplitudes of the non-archimedean open string are derived. These amplitudes can be generated from a simple non-local lagrangian involving a single scalar field (the tachyon) in ambient space-time. This lagrangian is studied and is found to possess a tachyon free vacuum with no “particles” but with soliton solutions. The question of generalizing the adelic product formular to N-point amplitudes is taken up. The infinite product of 5-point amplitudes is shown to converge in a suitably chosen kinematic region whence it can be analytically continued. Though the precise form of the product formula for the 5-point (and N-point)amplitudes is not found, it is shown that the product is not equal to one as it is for the 4-point amplitudes but rather involves the famous zeros of the Riemann zeta function. Chan-Paton rules for non-archimedean open strings are given. A string over the (global) field of rational numbers is constructed. Other problems that are addressed are the introduction of supersymmetry, the nature of a p-adic string lagrangian, and the possibility of strings over other locally compact fields.     

Higgs masses in the standard,multi-Higgs and supersymmetric models

Theoretical constraints and limits on the masses of Higgs scalars in the standard electroweak model, in electroweak models with additional Higgs doublets and in various supersymmetric models are presented. In the standard model, the lower limit on the Higgs mass, based on vacuum stability arguments, is reviewed in detail, as are “upper limits” based on perturbative constraints. In most grand unified and all supersymmetric models, however, at least two doublets are needed. The masses of the various Higgs scalars in the two-doublet model are discussed and constraints on their masses are found, including the generalization of the above limits. The results are then generalized to models with more than two doublets. Finally, recent attempts at constructing models with low-energy supersymmetry are reviewed and it is shown that in many models, fairly stringent tree-level mass relations among the Higgs scalars can be found. These relations are interesting in that they do not refer to the supersymmetric partners of ordinary particles, and they are most restrictive in models in which the supersymmetry is explicitly broken, i.e., via arbitrary mass terms.     

An alternative for moduli stabilisation

The one-loop vacuum energy is explicitly computed for a class of perturbative string vacua where supersymmetry is spontaneously broken by a T-duality invariant asymmetric Scherk–Schwarz deformation. The low-lying spectrum is tachyon-free for any value of the compactification radii and thus no Hagedorn-like phase-transition takes place. Indeed, the induced effective potential is free of divergence, and has a global anti-de Sitter minimum where geometric moduli are naturally stabilised.     

Ghost vertices for the bosonic string using the group-theoretic approach to string theory

The N-string tree-level scattering vertices for the bosonic string are extended to include anticommuting (ghost) oscillators. These vertices behave correctly under the action of the BRST charge Q and reproduce the known results for the scattering of physical states. This work is an application of the group-theoretic approach to string theory.     

Determinants,torsion, and strings

We apply the results of [BF1, BF2] on determinants of Dirac operators to String Theory. For the bosonic string we recover the “holomorphic factorization” of Belavin and Knizhik. Witten's global anomaly formula is used to give sufficient conditions for anomaly cancellation in the heterotic string (for arbitrary background spacetimes). To prove the latter result we develop certain torsion invariants related to characteristic classes of vector bundles and to index theory.     

Instanton effects in N = 2 supersymmetric quantum mechanics

Supersymmetric quantum mechanics with several bosonic and fermionic dynamic variables is considered. Two different N = 2 supersymmetric models involving instantons are discussed in detail. Instantons fail to break supersymmetry in one of the models considered. The vacuum state is degenerate in this model which generally results in spontaneous breaking of internal left-right symmetry. In another model supersymmetry is destroyed dynamically due to special complex instanton solutions. Possible implications for SUSY field theories are discussed.     

Conformal invariance of σ-models and classical string physics

We show that the identification of the conformal anomaly of the general bosonic two-dimensional non-linear σ-model as the generating functional for on-shell string scattering amplitudes is correct up toO(α′) terms. The absence, in the loop corrections to the spacetime effective action, of contributions from the explicit coupling to the dilaton field is suggested as a general feature for σ-models describing tree-level string physics.     

D-brane solutions in a light-like linear dilaton background

The light-like linear dilaton background presents a simple time dependent solution of type II supergravity equations of motion that preserves 1/2 supersymmetry in ten dimensions. We construct supergravity D-brane solutions in a linear dilaton background starting from the known intersecting brane solutions in string theory. By applying a Penrose limit on the intersecting (NS1–NS5–NS5′)-brane solution, we find out a D5-brane in a linear dilaton background. We solve the Killing spinor equations for the brane solutions explicitly, and show that they preserve 1/4 supersymmetry. We also find a M5-brane solution in eleven-dimensional supergravity.     

A heterotic N=2 string with space–time supersymmetry

We reconsider the issue of embedding space–time fermions into the four-dimensional N=2 worldsheet supersymmetric string. A new heterotic theory is constructed, taking the right-movers from the N=4 topological extension of the conventional N=2 string but a c=0 conformal field theory supporting target-space supersymmetry for the left-moving sector. The global bosonic symmetry of the full formalism proves to be U(1,1), just as in the usual N=2 string. Quantization reveals a spectrum of only two physical states, one boson and one fermion, which fall in a multiplet of (1,0) supersymmetry.     

Some phenomenological implications of string loop effects

We investigate low energy implications of string loop corrections to supergravity couplings which break a possible flavor universality of the tree level. If supersymmetry is broken by the dilaton F-term, universal soft scalar masses arise at the leading order but string loop corrections generically induce flavor-non-diagonal soft terms. Constraints from flavor changing neutral currents (FCNC) and CP violation then require a large supersymmetry breading scale and thus heavy gluinos and squarks. If supersymmetry is broken by moduli F-terms, universality at the string tree level can only be guaranteed by extra conditions on the Kahler potential. A large hierarchy between the gluino and squark masses ensures that FCNC and CP-violation constraints are satisfied. If the soft scalar masses vanish at the string tree level, the cosmological problems related to light moduli can be evaded. However, generic string loop corrections violate FCNC bounds and require very heavy squark masses (∼ 100 TeV).     

Nonlinear supersymmetry without the GSO projection and unstable D9-brane

Orientable open string theories containing both bosons and fermions without the GSO projection are expected to have the 10-dimensional N=2 space–time supersymmetry in a spontaneously broken phase. We study the low-energy theorem for the nonlinearly realized N=2 supersymmetry using the effective action for an unstable D9-brane. It is explicitly confirmed that the 4-fermion open string amplitudes without the GSO projection obey the low-energy theorem derived from the nonlinear N=2 supersymmetry. An intimate connection between the existence of the hidden supersymmetry and the open–open string (s–t) duality is pointed out.     

Pseudo-supersymmetry, consistent sphere reduction and Killing spinors for the bosonic string

Certain supergravity theories admit a remarkable consistent dimensional reduction in which the internal space is a sphere. Examples include type IIB supergravity reduced on S⁵, and eleven-dimensional supergravity reduced on S⁴ or S⁷. Consistency means that any solution of the dimensionally-reduced theory lifts to give a solution in the higher dimension. Although supersymmetry seems to play a role in the consistency of these reductions, it cannot be the whole story since consistent sphere reductions of non-supersymmetric theories are also known, such as the reduction of the effective action of the bosonic string in any dimension D on either a 3-sphere or a (D−3)-sphere, retaining the gauge bosons of SO(4) or SO(D−2) respectively. We show that although there is no supersymmetry, there is nevertheless a natural Killing spinor equation for the D-dimensional bosonic string. A projection of the full integrability condition for these Killing spinors gives rise to the bosonic equations of motion (just as happens in the supergravity examples). Thus it appears that by extending the notion of supersymmetry to “pseudo-supersymmetry” in this way, one may be able to obtain a broader understanding of a relation between Killing spinors and consistent sphere reductions.     

Cancellation of leading divergences in multiloop closed superstring amplitudes

We discuss the general problem of divergences and the particularly important “tadpole” configuration for multiloop amplitudes in the closed superstring - or heterotic string - covariant theory, with any number of external legs. We show that, due to a factor coming from the supermoduli, the tachyon divergence in the tadpole is cancelled in each spin structure contribution separately.     

Supersymmetry and positive temperature for simple systems

It has recently been argued by Girardello et al. that supersymmetry is automatically broken at positive temperature even when unbroken at T = 0, in the sense that the usual derivation of identities from unbroken supersymmetry does not automatically generalize to T > 0. Using as a guide simple examples with one bosonic and one fermionic degree of freedom, we study how supersymmetry reflects itself in the properties of excited states, in particular in the thermal properties at positive temperature. We derive a class of relations [see eq. 1.2)] which extend to all T the familiar consequences of unbroken supersymmetry for ground-state expectation values; these relations hold for unbroken and spontaneously broken supersymmetry. With Levine and Tomozawa we consider the algebra generated by the supercharges. In the case of two supercharges it can be reduced to the Clifford algebra of Pauli spin matrices, for which the eigenstates form irreducible doublets, except that a zero-energy eigenstate may be a singlet. The relations mentioned above are shown to hold for each doublet individually [see eq. (4,7)]. Some additional remarks are made on supersymmetry breaking at zero and positive temperatures.