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Register a new userDynamical Symmetry Breaking with Four-Superfield Interactions
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We investigate the dynamical mass generation resulted from interaction terms with four chiral superfields. The kind of interactions maybe considered a supersymmetric generalization of the four-fermion interactions of the classic Nambu--Jona-Lasinio model. A four-superfield interaction that contains a four-fermion interaction as one of its component terms has been the standard supersymmetrization of the NJL model for decades. Recently, we introduced a holomorphic variant with a dimension five interaction term instead. The latter is a main target of the present analysis. With the introduction of a new perspective on the superfield gap equation, we derive it for each one of the four-superfield interactions, using the supergraph technique. Through analyzing solutions to the gap equations, we illustrate the dynamical generation of superfield Dirac mass, including a supersymmetry breaking part. A dynamical symmetry breaking generally goes along with the dynamical mass generation, for which a bi-superfield condensate is responsible. The explicit illustration of dynamical symmetry breaking from the holomorphic dimension five interaction is reported for the first time. It has rich and novel features, which would be easily missed without the superfield approach developed here. We also discuss the nature of the bi-superfield condensate and its role of the effective Higgs superfield picture for both cases, illustrating their difference. Note that such a holomorphic quark superfield interaction term can successful account for the electroweak symmetry breaking with Higgs superfields as composites.
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In this paper we discuss Nambu-Jona-Lasinio model as a classical model for dynamical mass generation and symmetry breaking. In addition we discuss the possible supersymmetric extensions of this model resulting from interaction terms with four chiral superfields that may be regarded as a supersymmetric generalization of the four-fermion interactions of the Nambu-Jona-Lasinio model. A four-superfield interaction terms can be constructed as either dimension 6 or dimension 5 operators. Through analyzing solutions to the gap equations, we discuss the dynamical generation of superfield Dirac mass, including a supersymmetry breaking part. A dynamical symmetry breaking generally goes along with the dynamical mass generation, for which a bi-superfield condensate is responsible.
We derive all possible symmetry breaking patterns for all possible Higgs fields that can occur in intersecting brane models: bi-fundamentals and rank-2 tensors. This is a field-theoretic problem that was already partially solved in 1973 by Ling-Fong Li. In that paper the solution was given for rank-2 tensors of orthogonal and unitary group, and U(N x U(M) and O(N) x O(M) bi-fundamentals. We extend this first of al to symplectic groups. When formulated correctly, this turns out to be straightforward generalization of the previous results from real and complex numbers to quaternions. The extension to mixed bi-fundamentals is more challenging and interesting. The scalar potential has up to six real parameters. Its minima or saddle points are described by block-diagonal matrices built out of K blocks of size p x q. Here p=q=1 for the solutions of Ling-Fong Li, and the number of possibilities for p x q is equal to the number of real parameters in the potential, minus 1. The maximum block size is p x q=2 x 4. Different blocks cannot be combined, and the true minimum occurs for one choice of basic block, and for either K=1 or K maximal, depending on the parameter values.
We investigate cubic interactions between a chiral superfield and higher spin superfield corresponding to irreducible representations of the $4D,, mathcal{N}=1$ super-Poincar{e} algebra. We do this by demanding an invariance under the most general transformation, linear in the chiral superfield. Following Noethers method we construct an infinite tower of higher spin supercurrent multiplets which are quadratic in the chiral superfield and include higher derivatives. The results are that a single, massless, chiral superfield can couple only to the half-integer spin supermultiplets $(s+1,s+1/2)$ and for every value of spin there is an appropriate improvement term that reduces the supercurrent multiplet to a minimal multiplet which matches that of superconformal higher spins. On the other hand a single, massive, chiral superfield can couple only to higher spin supermultiplets of type $(2l+2hspace{0.3ex},hspace{0.1ex}2l+3/2)$ and there is no minimal multiplet. Furthermore, for the massless case we discuss the component level higher spin currents and provide explicit expressions for the integer and half-integer spin conserved currents together with a R-symmetry current.
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We study ${cal N}=1$ supersymmetric $Spin(10)$ chiral gauge theories with a single spinor representation and $N$ vector representations. We present a dual description in terms of an ${cal N}=1$ supersymmetric $SU(N-5)$ chiral gauge theory with a symmetric tensor, one fundamental and $N$ antifundamental representations. The $Spin(10)$ theory with $N=0$ breaks supersymmetry at strong coupling; we study how this arises at weak coupling in the dual theory, which is a spontaneously broken gauge theory. Also, we recover various known dualities, find new dual pairs and generate new examples of dynamical supersymmetry breaking.
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