Preheating and vacuum metastability in supersymmetry

The constraints imposed by the requirement that the scalar potential of supersymmetric theories does not have unbounded directions and charge or color breaking minima deeper than the usual electroweak breaking minimum (EWM) are significantly relaxed if one just allows for a metastable EWM but with a sufficiently long lifetime. For this to be acceptable one needs however to explain how the vacuum state reaches this metastable configuration in the first place. We discuss the implications for this issue of the inflation induced scalar masses, of the supersymmetry breaking effects generated during the preheating stage as well as of the thermal corrections to the scalar potential which appear after reheating. We show that their combined effects may efficiently drive the scalar fields to the origin, allowing them to then evolve naturally towards the EWM.     

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.     

Dynamical breaking of supersymmetry and positivity of vacuum energy density

The possibility of dynamical breaking of supersymmetry is investigated with special emphasis on the role of the positivity of the vacuum energy density. We point out that (i) the vacuum energy density can become negative after appropriate renormalization of the fields (thereby being energetically favorable over the supersymmetric case), yet (ii) in such a situation the Nambu-Goldstone fermion state must necessarily possess negative norm, the theory becoming physically unacceptable. This phenomenon is explicitly demonstrated using an O(N) symmetric Wess-Zumino type model in the large-N limit. We conclude that for dynamical breaking of supersymmetry to occur in a physically acceptable manner, it is necessary that supersymmetric solution(s) be completely destroyed. Our study suggests that a strong power-type infrared singularity might achieve such a situation.     

Dynamical properties of the vacuum in non-abelian field theories with and without supersymmetry

In QCD with massless quarks, the effective potential for the color singlet operator (F_μν^a)² can be constructed by the use of the trace anomaly equation and tells us that magnetic gluon condensation, 〈0|(F_μν^a)²|0〉 > 0, occurs. When the method is applied to supersymmetric QCD, however, it gives us a puzzle; the gluons condense with negative energy density, and supersymmetry is broken in a pathological manner with the appearance of a negatively normed Nambu-Goldstone fermion. Spurred on by this observation, we examine in detail the properties of the vacuum for the super (and ordinary) O(N) non-linear σ model in two dimensions for which a similar puzzling situation occurs with regard to the lagrangian condensate. We find, in particular, that (i) the chiral condensate plays a crucial role in resolving the puzzle and that (ii) it is the nature of the response of the lagrangian condensate to the test charge, not the sign or the magnitude of the condensate itself, that determines the phase of the system. Implications of these results for (super) QCD, including an unconventional possibility of “electric” gluon condensation, are discussed.     

Temperature and supersymmetry

We study equal-time correlation functions at finite temperature in field theories with global supersymmetry. Global supersymmetry is found to be broken at finite temperature; the ground state is not supersymmetric but no Goldstone fermion appears. The temperature dependence of the mass spectrum in the one-loop approximation and leading order in temperature is investigated in several models. In the models that we consider with spontaneous supersymmetry breaking we find that the Goldstone fermion remains massless at the one-loop level. Ward identities describing the supersymmetry of the underlying theory are checked at the one-loop level. We also discuss the situation in supergravity.     

Higgs and supersymmetry

Global frequentist fits to the CMSSM and NUHM1 using the MasterCode framework predicted M _h ?119 GeV in fits incorporating the (g?2) _μ constraint and ?126 GeV without it. Recent results by ATLAS and CMS could be compatible with a Standard Model-like Higgs boson around M _h ?125 GeV. We use the previous MasterCode analysis to calculate the likelihood for a measurement of any nominal Higgs mass within the range of 115 to 130 GeV. Assuming a Higgs mass measurement at M _h ?125 GeV, we display updated global likelihood contours in the (m ₀,m _1/2) and other parameter planes of the CMSSM and NUHM1, and present updated likelihood functions for $m_{\tilde{g}}, m_{\tilde{q}_{R}}We perform a determination of the strong coupling constant using the latest ATLAS inclusive jet cross section data, from proton?Cproton collisions at $\sqrt{s}=7~\mathrm{TeV}$ , and their full information on the bin-to-bin correlations. Several procedures for combining the statistical information from the different data inputs are studied and compared. The theoretical prediction is obtained using NLO QCD, and it also includes non-perturbative corrections. Our determination uses inputs with transverse momenta between 45 and 600?GeV, the running of the strong coupling being also tested in this range. Good agreement is observed when comparing our result with the world average at the Z-boson scale, as well as with the most recent results from the Tevatron.     

Fractional supersymmetry as a superposition of ordinary supersymmetry

It is shown how to derive fractional supersymmetric quantum mechanics of order k as a superposition of k-1 copies of ordinary supersymmetric quantum mechanics.     

Low-energy supersymmetry

We discuss the problem of constructing a model in which supersymmetry is unbroken down to low energies. It is suggested that the scalar partners of quarks and leptons may get their masses through radiative corrections and that the breaking of the weak interactions also occurs through radiative corrections. A toy model is constructed which illustrates these ideas.     

Unconstrained supersymmetry

This is a first step towards better superfield formulations of supersymmetric field theories. The simple Wess-Zumino model (including renormalizable interactions) is formulated in terms of an unconstrained, scalar superfield, obeying a wave equation that includes the square of the super Klein-Gordon operator. This wave equation is derived from an action principle, by unconstrained variation of the superfield. The physical content of the theory is the same as for the original formulation by Wess and Zumino, and the Feynman rules are identical to those of Grisaru, Roek and Siegel. Next, super electrodynamics, including minimal interactions with a scalar matter multiplet, is given a similar treatment. There is no need, in this case, to include higher derivatives in the Lagrangian. The matter field is an unconstrained, scalar superfield, and the gauge fields are also contained in an unconstrained, scalar superfield. The scattering matrix coincides with that of the conventional form of super electrodynamics with Wess-Zumino matter fields. Supersymmetric spinorial currents are found by simple and direct application of the Noetherian method, in superfield language. Conservation laws of the formD _a J ^a =0 (resp.D _a J ^ab =0) are derived from gauge invariance (resp. supersymmetry). Extension to super Yang-Mills theories is straightforward.On leave of absence from Universidad Complutense, Madrid. Permanent address: Department of Theoretical Physics, Universidad Complutense, 28040 Madrid, Spain.     

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.     

Dimensional regularization and supersymmetry

A detailed numerical integration of the Oppenheimer-Volkoff equations for isothermal partially degenerate neutral lepton configurations shows that the mass distribution of the dark halo around the giant elliptical galaxy M87, as revealed by X-ray observations, can be very naturally accounted for, in detail, by an atmosphere of (10–50 eV) neutrinos.     

Fermion flows and supersymmetry

Even fermionic stochastic flows are shown to be closely related to the mathematics of supersymmetry.     

Vacuum stability and supersymmetry

Radiative effects are shown to cause breakdown of the semiclassical ground state in a massless theory of fermions and spinless bosons when the coupling of fermions to bosons is larger than the boson self-coupling. Supersymmetry forms the boundary, in coupling constant space, separating theories with and without stable semiclassical vacua.     

Non-minimal and non-universal supersymmetry

I motivate and discuss non-minimal and non-universal models of supersymmetry and supergravity consistent with string unification at 10¹⁰ GeV.     

Strong gravity and supersymmetry

We construct a supersymmetric theory for a strong f- plus a weak g-graviton, together with their accompanying massive gravitinos, by gauging the graded OSp(2, 2, 1) × OSp(2, 2, 1) structure. The mixing term between f- and g-fields, which makes the strong graviton massive, can be introduced through a spontaneous symmetry-breaking mechanism implemented in this paper by constructing a non-linear realization of the symmetry group.     

Dimensional regularization and supersymmetry

We examine in detail the techniques of supersymmetric dimensional regularization. A peculiar complementarity is found to be inherent in the regularization: its manifestly supersymmetric version is contradictory, while the removal of inconsistencies costs a lossof supersymmetry in higher orders. We analyse this phenomenon at the level of Feynman diagrams and discover an explicit example of supersymmetry breakdown in the three-loop approximation. In the light of this result, we reconsider the status of dimensional regularization in globally supersymmetric gauge theories.