On higher derivative corrections of tachyon action

We have examined the momentum expansion of the disk level S-matrix element of two tachyons and two gauge fields to find, up to on-shell ambiguity, the couplings of these fields in the world volume theory of N coincident non-BPS D-branes to all order of α^′. Using the proposal that the action of D-brane–anti-D-brane is given by the projection of the action of two non-BPS D-branes with (−1)^F_L, we find the corresponding couplings in the world volume theory of the brane–anti-brane system. Using these infinite tower of couplings, we then calculate the massless pole of the scattering amplitude of one RR field, two tachyons and one gauge field in the brane–anti-brane theory. We find that the massless pole of the field theory amplitude is exactly equal to the massless pole of the disk level S-matrix element of one RR, two tachyons and one gauge field to all order of α^′. We have also found the couplings of four tachyons to all order of α^′ by examining the S-matrix element of four tachyons.     

On the vacuum rearrangement in massless chromodynamics

It is shown that in the weak coupling limit the Bethe-Salpeter equation of massless chromodynamics admits a colourless tachyon solution when the number of quark multiplets n ? n_c, where for the colour group SU(N) the critical value n_c ≈ 0.14 N³/(N² ? 1). When n ? n_c, the vacuum rearrangement results in the gluons acquiring a mass; n > n_c all particles remain massless.     

Breaking of the SO(n) symmetry with vector and adjoint higgses

The spontaneous symmetry breaking of SO(n) is investigated by studying the most general quartic SO(n)-invariant Higgs potential with two multiplets of scalars belonging to a vector and to an adjoint representation. In the most general cases largest residual symmetry is found to be SU(l), SU(l-1), SO(l), SO(l-1) or SO(n-2) wherel is the rank of SO(n). In particular, the breaking of SO(n) into SU(n ₁)×SU(n ₂) is found to occur only in special cases.     

Stability of instanton-induced compactification in 8 dimensions

We consider the 8-dimensional Einstein-SU(2) Yang-Mills system when the Yang-Mills system assumes a 1-instanton configuration on an internal S₄ with the vacuum solution possessing the geometry of M₄ × S₄ and the invariance group P₄(Poincaré) × SO(5). We demonstrate the classical stability of the solution by computing the spectrum of the physical states and showing the absence of ghosts and tachyons amongst them. We also discuss the possibility of obtaining SO(5) multiplets of massless fermions.     

The criterion for vacuum stability in Kaluza-Klein supergravity

We prove that in the spectrum of the d = 4 theory obtained by Freund-Rubin compactification of d = 11 superconductivity, only fields of spin 0⁺ can give rise to classical instabilities. The criterion for stability in the 0⁺ sector can be expressed as a certain lower bound on the Lichnerowicz operator Δ_L on the d = 7 compact space. Thus not only are supersymmetric vacua always stable but so are the corresponding non-supersymmetric vacua obtained by reversing the orientation of the compact space, since the 0⁺ spectrum is insensitive to the orientation. Examples are the orientation-reversed spaces with N = 0 obtained from the squashed seven-sphere with N = 1 and from SU(3) ×SU(2) ×U(1) spaces with N = 2 supersymmetry. Product spaces, on the other hand, are always unstable. Finally, we examine the massless sectors of the squashed seven-sphere vacua, and find an additional 135 massless scalars.     

A scenario for SUSY QCD

The following scenario is proposed for supersymmetric QCD: With massless (s) quarks, there is a continuum of vacua, including one with all global symmetries unbroken; with (s) quarks of mass m, there is a unique vacuum, no Goldstone bosons, but a rich spectrum of scalars and fermions of mass O(m). Consistency with various non-perturbative requirements is exhibited.     

Four loop massless propagators: An algebraic evaluation of all master integrals

The old “glue-and-cut” symmetry of massless propagators, first established in Ref. [1] (Chetyrkin and Tkachov, 1981), leads — after reduction to master integrals is performed   — to a host of non-trivial relations between the latter. The relations constrain the master integrals so tightly that they all can be analytically expressed in terms of only few, essentially trivial, watermelon-like integrals. As a consequence we arrive at explicit analytical results for all master integrals appearing in the process of reduction of massless propagators at three and four loops. The transcendental structure of the results suggests a clean explanation of the well-known mystery of the absence of even zetas (ζ_2n${\zeta }_{2n}$) in the Adler function and other similar functions essentially reducible to massless propagators. Once a reduction of massless propagators at five loops is available, our approach should be also applicable for explicitly performing the corresponding five-loop master integrals.     

Radiatively induced spontaneous symmetry breaking and phase transitions in curved spacetime

Local gauge symmetries which are spontaneously broken in flat spacetime are shown to be restored for large spacetime curvatures. The case of symmetry breaking due to radiative quantum corrections in gauge theories with elementary scalar fields is considered explicitly. In spacetimes with a positive Ricci curvature scalar R and a cosmological event horizon, the critical curvature R_C is of O(m_H²) or O(m_W²), depending on whether the theory is formulated with conformal or minimal scalar fields. In Ricci flat spacetimes with a conventional event horizon the symmetry is expected to be restored when the temperature of the Hawking thermal radiation is of O(m_W). This phenomenon is described in detail, using functional integral methods and dimensional renormalization, for massless scalar electro-dynamics in de-Sitter spacetime. For conformal scalars, the symmetry restoring phase transition is first order, the critical curvature being R_C = 0.910 m_H². For minimal scalars, an anomalous, curvature dependent mass counterterm is required. The phase transition in this case is second order, and occurs at R_C = 83.57 m_W². Symmetry restoration at finite temperature in flat spacetime is considered in an appendix. The critical temperature at which a first-order phase transition occurs in the Weinberg-Salam model is found to be T_C = 0.329 m_W.     

Critical behaviour of SU(n) quantum chains and topological non-linear σ-models

The critical behaviour of SU(n) quantum “spin” chains, Wess-Zumino-Witten σ-models and grassmanian σ-models at topological angle θ = π (of possible relevance to the quantum Hall effect) is reexamined. It is argued that an additional Z_n symmetry is generally necessary to stabilize the massless phase. This symmetry is not present for the σ-models for n > 2 and is only present for certain representations of “spin” chains.     

Cosmological consequences of grand unification beyond SU(5)

We examine the cosmological consequences of new types of fermions generally present in GUTs based on unitary groups larger than SU(5) which break down to SU(5) at ultralarge energies. We find that some SU(5) singlet fermions in such theories tend to have masses small compared to 10¹⁵ GeV. If sufficiently light (or massless) such particles affect He abundance unacceptably. If heavier (but still light compared to 10¹⁵ GeV) the decays of such particles generate entropy and thus greatly suppress n_B/n_γ.Such theories also contain ultraheavy fermions. Their decays are shown to be a prime source of singlet fermions. It is also shown that the decays of ultraheavy fermions generate entropy which tends to suppress the contribution to n_B/n_γ from usual mechanisms. These decays may themselves, however, generate a baryon asymmetry.     

Superstring theory

Dual string theories, initially developed as phenomenological models of hadrons, now appear more promising as candidates for a unified theory of fundamental interactions. Type I superstring theory (SST I), is a ten-dimensional theory of interacting open and closed strings, with one supersymmetry, that is free from ghosts and tachyons. It requires that an SO(n) or Sp(2n) gauge group be used. A light-cone-gauge string action with space-time supersymmetry automatically incorporates the superstring restrictions and leads to the discovery of type II superstring theory (SST II). SST II is an interacting theory of closed strings only, with two D = 10 supersymmetries, that is also free from ghosts and tachyons. By taking six of the spatial dimensions to form a compact space, it becomes possible to reconcile the models with our four-dimensional perception of spacetime and to define low-energy limits in which SST I reduces to N = 4, D = 4 super Yang-Mills theory and SST II reduces to N = 8, D = 4 supergravity theory. The superstring theories can be described by a light-cone-gauge action principle based on fields that are functionals of string coordinates. With this formalism any physical quantity should be calculable. There is some evidence that, unlike any conventional field theory, the superstring theories provide perturbatively renormalizable (SST I) or finite (SST II) unifications of gravity with other interactions.     

Massless chiral families in superstring theories

The contribution of the U(1) and simple group factors S_k of the background gauge group ifS=Π_kS_k to the number of massless fermion generations in superstrings theories is examined. Unlike the semisimple case when only SU(n) factors contribute to the generation number, if the abelian factors are present, all groups contained in S contribute to it.     

The one-loop Green’s functions of dimensionally reduced gauge theories

We apply the dimensional regularization technique as well as that by dimensional reduction to the calculation of the regularized one-loop Green’s functions ind ₀-dimensional Yang-Mills theory with real massless scalars and spinors in arbitrary (real) representations of a gauge groupG. As a particular example, the super-symmetrically regularized one-loop Green’s functions of theN=4 supersymmetric Yang-Mills model are derived.     

Logarithmic divergence in four-dimensional string theory

Logarithmic divergences in the one-loop scattering amplitude of the heterotic string compactified on the Z_n-orbifold are investigated. The coefficient of these divergences is shown to be a function of the indices of the representations to which the massless states of the model belong.     

SU(3)×SU(2)×U(1) next-to-leading corrections for proton decay in the SU(5) model

We compute in the standard model of SU(3)^c×(SU(2)×U(1)) with massless quarks and leptons the two-loop anomalous dimensions of the four-fermion operators relevant to proton decay in process involving (u, d, e, ν_e). The calculation is carried out by the use of dimensional reduction, a variant of dimensional regularization. Our aim is to give a complete calculation within the SU(5) GUT model of the next-to-leading enhancement-suppression factor for nucleon decay due to renormalization effects arising from hard gluons, W's and B's in process which involve (u, d, e, ν_e). It turns out that the result is sensitive to the ratios x_(i) = M_{H (i)}/M_X where M_H(i) are the masses of the twelve superheavy Higgs scalars in the $\text{24}$ multiplet which breaks SU(5) → SU(3)×SU(2)×U(1).     

Anomaly cancelling terms from the elliptic genus

We calculate the heterotic string one-loop diagram in 2n + 2 dimensions with one external B_μν and n external gravitons and/or gauge bosons. The result is a modular integral over the weight zero terms of the character valued partition function (or elliptic genus) of the theory, and can be directly expressed in terms of the factor which multiplies TrF² − TrR² in the field theory anomaly. The integrands have a non-trivial dependence on the modular parameter τ, reflecting contributions not only from the physical massless states but also from an infinity of “unphysical” modes. Some of them are identical to integrands which have been discussed recently in relation with Atkin-Lehner symmetry and the cosmological constant. As a corollary we find a method to compute these integrals without using Atkin-Lehner transformations.     

The n-loop expansion of the Reggeon calculus

We apply the technique known in solid state physics as the n-loop expansion to calculate the critical indices of the φ³ Gribov Reggeon calculus directly in two transverse dimensions. Infrared pathologies of the massless theory require the calculation to be done in the infinite momentum limit of the massive theory. For n = 1 the results are close to those of the ε-expansion in O(ε). For n = 2 the β function has no zero, analogously to the case in solid state physics. Use of a Padé approximant for β yields σ_tot ≈ (1n s)^0.27 at infinity, close to the O(ε²) result.     

Non-perturbative renormalization group for field theories with scalars and fermions

An approximate, but non-perturbative, RG equation is derived for theories involving scalars and fermions, ind dimensions withn _f flavours. The approximation consists in restricting the parameter space to interactions without derivatives. In a numerical study of the equation ind=3 andd=4, in the range of parameter space explored, no evidence is found of new fixed points generated by the inclusion of fermions.     

Smooth mass corrections to massless theories

We analyze the transition from massive to massless theories in cases in which mass singularities are present. In massless theories these singularities are absorbed into densities or fragmentation functions. We define a subtraction procedure for massive theories which is a canonical generalization of the “minimal subtraction” in massless theories. We use this procedure to calculate smooth mass corrections to the structure functionsF ₂ andG ₁ of deep inelastic scattering. In particular we show how, in our scheme, heavy quarks affect the spin of the proton.