Algebraic renormalization of N = 1 supersymmetric gauge theories (original) (raw)
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Journal of High Energy Physics, 1998
The supercurrent components of the N = 1, D = 4 Super-Yang-Mills theory in the Wess-Zumino gauge are coupled to the components of a background supergravitation field in the "new minimal" representation, in order to describe the various conservation laws in a functional way through the Ward identities for the diffeomorphisms and for the local supersymmetry, Lorentz and R-transformations. We also incorporate in the same functional formalism the supertrace identities, which leads however to a slight modification of the new minimal representation for supergravity, thus leading to a conformal version of it. The most general classical action obeying all the symmetry constraints and the condition of power-counting renormalizability is constructed.
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A new, simplified method for calculating the renormalization group equations for scalar fields is presented. The method is based on the renormalization of the effective potential as a whole. The two-loop equations for a general theory are given, and the example of the adjoint representation of SU(n) is considered in detail. It is found to differ substantially from the more common example of the fundamental representation.
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We reconsider the algebraic BRS renormalization of Witten's topological Yang-Mills field theory by making use of a vector supersymmetry Ward identity which improves the finiteness properties of the model. The vector supersymmetric structure is a common feature of several topological theories. The most general local counterterm is determined and is shown to be a trivial BRS-coboundary.
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N = 1 supersymmetric gauge theories with global flavor symmetries contain a gauge invariant W-superalgebra which acts on its moduli space of gauge invariants.
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We develop a new operator quantization scheme for gauge theories in which the dynamics of the ghost sector is described by an N=2 supersymmetry. In this scheme no gauge condition is imposed on the gauge fields. The corresponding path integral is explicitly Lorentz invariant and, in contrast to the BRST-BFV path integral in the Lorentz gauge, it is free of the Gribov ambiguity, i.e., it is also valid in the non-perturbative domain. The formalism can therefore be used to study the non-perturbative properties of gauge theories in the infra-red region (gluon confinement).
Renormalizability of non(anti)commutative gauge theories with Script N = 1/2 supersymmetry
Journal of High Energy Physics, 2003
Non(anti)commutative gauge theories are supersymmetric Yang-Mills and matter system defined on a deformed superspace whose coordinates obey non(anti)commutative algebra. We prove that these theories in four dimensions with N = 1 2 supersymmetry are renormalizable to all orders in perturbation theory. Our proof is based on operator analysis and symmetry arguments. In a case when the Grassman-even coordinates are commutative, deformation induced by non(anti)commutativity of the Grassman-odd coordinates contains operators of dimension-four or higher. Nevertheless, they do not lead to power divergences in a loop diagram because of absence of operators Hermitian-conjugate to them. In a case when the Grassman-even coordinates are noncommutative, the ultraviolet-infrared mixing makes the theory renormalizable by the planar diagrams, and the deformed operators are not renormalized at all. We also elucidate relation at quantum level between non(anti)commutative deformation and N = 1 2 supersymmetry. We point out that the star product structure dictates a specific relation for renormalization among the deformed operators.
Les Houches - Ecole d’Ete de Physique Theorique
We introduce simple and more advanced concepts that have played a key role in the development of supersymmetric systems. This is done by first describing various supersymmetric quantum mechanics models. Topics covered include the basic construction of supersymmetric field theories, the phase structure of supersymmetric systems with and without gauge particles, superconformal theories and infrared duality in both field theory and string theory. A discussion of the relation of conformal symmetry to a vanishing vacuum energy (cosmological constant) is included.
Supersymmetric gauge theories in quantum mechanics
Annals of Physics, 1985
A general construction for supersymmetric U( 1) gauge invariant Hamiltonians in quantum mechanics is given. For a given number of fermionic and bosonic degrees of freedom it is shown that for four supercharges the interactions are determined uniquely, and coincide with the dimensionally reduced N = 1, d= 3 + 1 supersymmetric electrodynamics. With two supercharges one gets models which cannot be obtained through dimensional reduction. For two special choices of a parameter one recovers the dimensionally reduced d= 1 + 1 Weyl supersymmetric and Majorana supersymmetric electrodynamics. 6
Supersymmetric gauge theories with a free algebra of invariants,” Nucl
1998
We study the low-energy dynamics of all N = 1 supersymmetric gauge theories whose basic gauge invariant fields are unconstrained. This set includes all theories whose matter Dynkin index is less than the index of the adjoint representation. We study the dynamically generated superpotential in these theories, and show that there is a W = 0 branch if and only if anomaly matching is satisfied at the origin. An interesting example studied in detail is SO(13) with a spinor, a theory with a dynamically generated W and no anomaly matching at the origin. It flows via the Higgs mechanism to SU(6) with a three-index antisymmetric tensor, a theory with a W = 0 branch and anomaly matching at the origin.