Infrared divergences and a non-local gauge for superspace Yang-Mills theory

The usual superspace approach to supersymmetric gauge theories suffers from problems with infrared divergences which greatly complicate multiloop calculations. We eliminate these divergences by introducing a non-local gauge-fixing term. In the background field method this term leads to unusual quantum-background interactions. Functional methods are presented for dealing with these interactions. As an example we compute the two-loop Yang-Mills β-function using the background field method in superspace. We also show how a non-local gauge can be used in ordinary, non-supersymmetric Yang-Mills theory.     

Cancellation of quadratically divergent mass corrections in globally supersymmetric spontaneously broken gauge theories

The one-loop quadratically divergent mass corrections in globally supersymmetric gauge theories with spontaneously broken abelian and non-abelian gauge symmetry are studied. Quadratically divergent mass corrections are found to persist in an abelian model with an ABJ anomaly. However, additional supermultiplets necessary to cancel the ABJ anomaly, turn out to be sufficient to eliminate the quadratic divergences as well, rendering the theory natural. Quadratic divergences are shown to vanish also in the case of an anomaly free model with spontaneously broken non-abelian gauge symmetry.     

Ultraviolet divergences in non-renormalizable supersymmetric theories

We present a pedagogical review of our current understanding of the ultraviolet structure of N = (1,1) 6D supersymmetric Yang–Mills theory and of N = 8 4D supergravity. These theories are not renormalizable, they involve power ultraviolet divergences and, in all probability, an infinite set of higherdimensional counterterms that contribute to on-mass-shell scattering amplitudes. A specific feature of supersymmetric theories (especially, of extended supersymmetric theories) is that these counterterms may not be invariant off shell under the full set of supersymmetry transformations. The lowest-dimensional nontrivial counterterm is supersymmetric on shell. Still higher counterterms may lose even the on-shell invariance. On the other hand, the full effective Lagrangian, generating the amplitudes and representing an infinite sum of counterterms, still enjoys the complete symmetry of original theory. We also discuss simple supersymmetric quantum-mechanical models that exhibit the same behaviour.     

Secret supersymmetry

We present new non-linear realizations of the N = 1 supergravity algebra. They allow us to build interesting realistic models of the four forces of nature. These models are different from all previous ones in that particles do not appear in (broken) supersymmetric multiplets.These new non-linear realizations also permit us to construct the effective low-energy lagrangian of an arbitrary supergravity theory in which supersymmetry is spontaneously broken. We are thus able to analyze what are the model-independent low-energy effects of supergravity. We find that the number of Higgs fields and the way they couple to quark and lepton matter is a feature which distinguishes supersymmetric theories from non-supersymmetric ones.     

The spectrum of a class of supersymmetric theories with false vacua

The spectrum of a supersymmetric quantum mechanics model, whose potential has a steep supersymmetric minimum and a broad non-supersymmetric minimum, is analyzed. With the exception of the supersymmetric ground state, the low-energy spectrum is found to be determined entirely by the non-supersymmetric well. The model is motivated by effective lagrangians proposed for supersymmetric QCD. It is speculated that in an equivalent field theory exhibiting a supersymmetric true vacuum and a non-supersymmetric false vacuum, the false vacuum can play an important rôle in the physics, and that the lowest energy excitations are extended field configurations involving a new mass scale.     

Positive energy without supersymmetry

Witten's positive energy theorem and its generalizations can be viewed as stating that supersymmetric solutions of any supergravity theory are stable. In this paper we give a criterion to test the stability of non-supersymmetric solutions of supergravity theories and solutions of theories which cannot be embedded in a supergravity theory. Previously some of these solutions might have been considered to be unstable. In particular, we show that the non-supersymmetric stationary point of the scalar potential of the gauged N = 5 supergravity theory is stable. We also give an elegant derivation of the Breitenlohner-Freedman condition for (small fluctuation) stability.     

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.     

Spectral properties in supersymmetric matrix models

We formulate a general sufficiency criterion for discreteness of the spectrum of both supersymmmetric and non-supersymmetric theories with a fermionic contribution. This criterion allows an analysis of Hamiltonians in complete form rather than just their semiclassical limits. In such a framework we examine spectral properties of various (1+0) matrix models. We consider the BMN model of M-theory compactified on a maximally supersymmetric pp-wave background, different regularizations of the supermembrane with central charges and a non-supersymmetric model comprising a bound state of N D2 with m D0. While the first two examples have a purely discrete spectrum, the latter has a continuous spectrum with a lower end given in terms of the monopole charge.     

Regularization by dimensional reduction of supersymmetric and non-supersymmetric gauge theories

We apply the technique of dimensional reduction to both supersymmetric and non-supersymmetric theories. Explicit one- and two-loop calculations show that in the latter case the technique is a viable alternative to conventional dimensional regularization, while in the former it preserves the Slavnov-Taylor identities of both supersymmetry and gauge invariance.     

Non-perturbative infinities

We investigate non-perturbative contributions to ultraviolet divergences in several field theories. Although we concentrate on finite theories with extended supersymmetry, we also present some results for asymptotically free theories. The N = 2 supersymmetric σ models that we study at the end of the paper are important in the theory of superstrings. Unfortunately, while we are able to rule out instanton contributions to the β functions of these theories, we do not have a complete non-perturbative proof that they are conformally invariant. Sigma models with N = 4 supersymmetry are shown to be both perturbatively and non-perturbatively finite.     

Dynamics of compositeW-bosons

We derive some constraints among the masses and couplings of theW-bosons and the vacuum condensates of some non-supersymmetric and supersymmetric theories where theW are composite particles. We deduce that in a theory where the value of the hypergluon condensate is much smaller than the value of the compositeness scale (like in the case of an unbroken supersymmetry), theW-bosons cannot be composite.     

Equivalent lagrangians in large N field theories

The auxiliary field method is generalized to any O (N)-invariant theory with non-polynomial interactions. In non-supersymmetric theories, two lagrangians with and without an auxiliary field are shown to be equivalent to the leading order of the 1/N expansion. In supersymmetric theories, these two lagrangians are equivalent to all orders of the 1/N expansion. The lagrangian with an auxiliary field is solvable in the 1/N expansion.     

Non-supersymmetric vacua and the D-flatness condition

Some N = 1 gauge theories, including SQED and N_F = 1 SQCD, have the property that, for arbitrary superpotentials, all stationary points of the potential V = F + D are D-flat. For others, stationary points of V are complex gauge transformations of D-flat configurations. As an implication, the technique to parametrize the moduli space of supersymmetric vacua in terms of a set of basic holomorphic G invariants can be extended to non-supersymmetric vacua. A similar situation is found in non-gauge theories with a compact global symmetry group.     

Prospects of experimentally reachable beyond Standard Model physics in inverse see-saw motivated <Emphasis Type="Italic">SO</Emphasis>(10) GUT

The grand unification theories based on SO(10) gauge group have been at the centre of attraction to beyond Standard Model phenomenology. The SO(10) gauge symmetry may pass through several intermediate symmetries before breaking to Standard Model. Therefore some higher symmetries may occur at the experimentally reachable scales. This feature flourishes easily in non-supersymmetric models compared to supersymmetric ones. We find that certain breaking chains give tremendous predictions for the physics being explored at various particle physics experiments. Explanation to neutrino masses through TeV scale inverse see-saw is the driving theme of the models studied.     

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.     

Predictivity of models with spontaneously broken non-Abelian discrete flavor symmetries

In a class of supersymmetric flavor models predictions are based on residual symmetries of some subsectors of the theory such as those of the charged leptons and neutrinos. However, the vacuum expectation values of the so-called flavon fields generally modify the Kähler potential of the setting, thus changing the predictions. We derive simple analytic formulae that allow us to understand the impact of these corrections on the predictions for the masses and mixing parameters. Furthermore, we discuss the effects on the vacuum alignment and on flavor changing neutral currents. Our results can also be applied to non-supersymmetric flavor models.     

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.     

Finite field theories in three dimensions with and without supersymmetry

Necessary and sufficient conditions are derived for the finiteness of theS-matrix and vacuum stress of theories with Yukawa,? ³, and? ⁴ couplings in three spacetime dimensions, and general supersymmetric solutions to these conditions are given. The requirement of a finiteS-matrix allows many non-supersymmetric solutions, but with two bosons and two fermions the additional constraint of a finite vacuum stress allows only one simple alternative to supersymmetry.     

Chiral dynamics and meson with non-commutative dipole field in gauge/gravity dual

Apply the T-duality and smeared twist to the D3-brane solution one can construct the supergravity backgrounds which may dual to supersymmetric or non-supersymmetric non-commutative dipole field theory. We introduce D7-brane probe into the dual supergravity background to study the chiral dynamics and meson spectrum therein. We first find that the non-commutative dipole field does not induce the chiral symmetry breaking even if the supersymmetry was completely broken, contrast to the conventional believing that the chiral symmetry will be broken in the non-supersymmetric theory. Next, we find that the dipole field does not modify the meson spectrum in the supersymmetric theory while it will reduce the meson bound-state energy in the non-supersymmetric theory. We also evaluate the static quark–anti-quark potential and see that the dipole field has an effect to produce attractive force between the quark and anti-quark.     

Anomaly constraints on supersymmetric effective lagrangians

In this paper we set constraints on the possible effective-lagrangian representations of supersymmetric gauge theories with spontaneously broken chiral flavor symmetries, by finding the conditions under which a Wess-Zumino term to represent the anomalous interactions can be constructed. We find that effective lagrangians for such theories are possible only for nonlinear sigma models defined on noncompact manifolds, and demonstrate the realization of this result in supersymmetric QCD. We also consider the Wess-Zumino term in the nonlinear realization of broken supersymmetry.