Spontaneous breakdown in two dimensional space-time

We prove that in two-dimensional space-time, symmetry transformations which are generated by Poincaré covariant currents can not be spontaneously broken. This is also the case with the dilation current. We argue that other currents which involve explicit space-time dependence might lead to spontaneously broken symmetries accompanied by massless Goldstone bosons. We construct a trivial example where this phenomenon occurs.     

Tachyon condensation for intersecting branes at small and large angles

We review the worldsheet analysis for intersecting branes with focus on small and large angles. For small angles, we review the Yang‐Mills fluctuation analysis in [1] and find an additional family of massless modes. They are the components of a Goldstone scalar corresponding to the spontaneously broken U(2)‐gauge symmetry. For branes at large angles, we derive an effective tachyon field theory from BSFT results. We show how the gauge symmetry of this system implies a mass spectrum which is consistent with the worldsheet analysis.     

Spontaneously broken quark helicity symmetry

We discuss the origin of chiral-symmetry breaking in the light-cone representation of QCD. In particular, we show how quark helicity symmetry is spontaneously broken in SU (N) gauge theory with massless quarks if that theory has a condensate of fermion light-cone zero modes. The symmetry breaking appears as induced interactions in an effective light-cone Hamiltonian equation based on a trivial vacuum. The induced interaction is crucial for generating a splitting between pseudoscalar and vector meson masses, which we illustrate with spectrum calculations in some 1 + 1-dimensional reduced models of gauge theory.     

Supersymmetry breaking in three dimensions

One-loop corrections to the effective potential in three-dimensional supersymmetric massless scalar electrodynamics are calculated to see whether or not they spontaneously break supersymmetry. It is found that neither the supersymmetry nor the U(1) gauge invariance is broken by one-loop effects.     

Vacuum instabilities in models with spontaneous symmetry breaking

Adopting as a reference a simple model with spontaneously broken symmetry we show that the extra massless field present in the three approximation in addition to the true Goldstone bosons may induce, through the radiative corrections to its vacuum expectation value, infrared effects which are not compensable without spoiling the symmetry itself. We further extend the analysis to generic lagrangian field models with spontaneous symmetry breaking and prove that the only constraint to their renormalizability arises from the radiative corrections to the vacuum expectation value of the massless fields, except for the true Goldstone bosons which never induce such pathologies.     

On the relation between the Abelian Higgs model and the spontaneously broken massless scalar electrodynamics

An analysis is made of the connection between the “massless” field theories, in the presence of the Coleman-Weinberg phenomenon and the corresponding models with a “negative mass” term as origin of the spontaneous breakdown. For the very interesting case of an Abelian gauge theory, i.e. the Higgs model, we find the conditions for the parameters of the theory which make it equivalent to the spontaneously broken scalar massless electrodynamics. The properties of the effective potential in this limit are studied.     

Non-existence of Goldstone bosons with non-zero helicity

In a local relativistic quantum field theory a conserved covariant tensor current may lead to a spontaneously broken symmetry if it generates zero mass states from the vacuum (Goldstone theorem). Here it is shown that in addition it is necessary that these massless states have helicity zero if the underlaying state space has a positive metric.     

Spontaneously broken supergauge symmetries and goldstone spinors

We present a model with a spontaneously broken supergauge symmetry which results in the appearance of a massless Goldstone spinor. The model combines supergauge invariance with ordinary gauge invariance. After the breaking the gauge boson acquires a mass as a result of the Higgs mechanism.     

Proof of Chiral Symmetry Breaking and Persistent Mass Condition in Vector- Like Gauge Theory

We give the details of rigorous proof of some mass inequalitiee in a vector-like gauge theory based on any simple group G. These mass inequalitiee lead to the conclusions that in auch a theory the chiral symmetries associated with all G representations of quarks must be spontaneously broken, and the persistent mass condition ie justified for any composite particles when the vacuum angle is zero or massless quarks exist.     

Spontaneous breakdown and finiteness of supersymmetric theories in two dimensions

Using a single scalar superfield we construct the two dimensional version of the four dimensional Wess-Zumino model and examine its renormalization properties. In the context of this model and in the tree approximation we find that supersymmetry can be spontaneously broken with the appearance of a massless fermion. This solution is then shown to be dynamically unstable at the one-loop level. Finally we use supersymmetry to construct two dimensional theories for which all IPI vertices are finite.     

Spontaneous symmetry breaking in massless field theories: Dimensional transmutation and gauge independence

In a reformulation of the Coleman and Weinberg program, we study the parametrization of the spontaneous symmetry breaking solutions of massless field theories. Our analysis is based on a full use of the concept of the dimensional transmutation, namely the parametrization in terms of the independent invariants of the underlying renormalization group. This invariant parametrization provides a convenient setting for the operator interpretation in a given Fock space and is shown to be a powerful tool in studying general aspects of the theory beyond the one-loop approximation. In particular, the gauge independence of the physical matrix elements in the spontaneously broken solution of massless scalar electrodynamics is demonstrated to all orders in perturbation theory.     

Quantum scale invariance,cosmological constant and hierarchy problem

We construct a class of theories which are scale-invariant on quantum level in all orders of perturbation theory. In a subclass of these models scale invariance is spontaneously broken, leading to the existence of a massless dilaton. The applications of these results to the problem of stability of the electroweak scale against quantum corrections, to the cosmological constant problem and to dark energy are discussed.     

Finite-temperature Hartree-Fock approximation to λΦ4 theory

The finite-temperature Hartee-Fock approximation to the effective potential for massless λΦ⁴ theory is calculated. The reflection symmetry which, in the same approximation, turns out to be spontaneously broken at zero temperature, is restored at a critical temperature. The nature of the phase transition is analyzed. A comparison with previous calculations is presented.     

de Sitter vacua via consistent terms

We introduce a new mechanism for producing locally stable de Sitter or Minkowski vacua, with spontaneously broken N = 1 supersymmetry and no massless scalars, applicable to superstring and M-theory compactifications with fluxes. We illustrate the mechanism with a simple N = 1 supergravity model that provides parametric control on the sign and the size of the vacuum energy. The crucial ingredient is a gauged U(1) that involves both an axionic shift and an R symmetry, and severely constrains the F- and D-term contributions to the potential.     

Impossibility of adding gauge couplings to spontaneously broken N = 8 supergravity

When the four mass parameters of spontaneously broken N = 8 supergravity are taken to be equal, the theory possesses at global SU(4) symmetry. Since it contains massless vectors in the adjoint representation, it is tempting to add gauge interactions so as to make the SU(4) symmetry local. In this paper we show that it is impossible to do this in a way that is consistent with the spontaneous character of the symmetry breaking.     

Effective lagrangian for spontaneously broken N = 2 superconformal symmetry

In a general framework of non-linear realizations for space-time symmetries, we investigate the effective lagrangian for N = 2 superconformal symmetry which is spontaneously broken down to N = 2 super-Poincaré symmetry. For the case in which the dilation multiplet is a massless N = 2 gauge multiplet, we derive a low-energy effective lagrangian which describes the interaction of Nambu-Goldstone particles.     

Spontaneous creation of massive spin half particles by a rotating block hole

The techniques of second quantization in Kerr metric for the scalar and neutrino (massless) fields are extended to the massive spin half case. The normal modes of Dirac field in Kerr metric are obtained in Chandrasekhar’s representation and the field is quantized as usual by imposing equal-time anti-commutation relations. The vacuum expectation value of energy-momentum tensor is evaluated asymptotically, leading to the result that a Kerr black hole spontaneously creates, in addition to scalar and neutrino quanta, massive Dirac particles in the classical superradiant modes.     

About the realization of chiral symmetry in QCD2

Two dimensional massless quantum chromodynamics presents many features which resemble those of the true theory. In particular the spectrum consists of mesons and baryons arranged in flavour multiplets without parity doubling. We analyze the implications of chiral symmetry, which is not spontaneously broken in two dimensions, in the spectrum and in the quark condensate. We study how parity doubling, an awaited consequence of Coleman's theorem, is avoided due to the dimensionality of space-time and confinement. We prove that a chiral phase transition is not possible in the theory.     

Massless QCD and chiral symmetry breaking

It is well known that chiral symmetry is spontaneously broken in QCD. To relate this fact to non-perturbative features of the theory, like instantons, we start with a massless lagrangian and perform a non-linear chiral colored singlet transformation on the quark fields which yields (by means of Fujikawa's method) essentially two terms in the lagrangian. First a quark mass term induced by instantons and secondly a coupling between pseudoscalar mesons and the axial anomaly. Ward-Takahashi identities can be derived. To clarify the presence of this induced mass term we calculate its first perturbative part up to the two-loop level.