Four dimensional supersymmetric theories in presence of a boundary (original) (raw)

Boundary effects in super-Yang–Mills theory

In this paper, we shall analyze a three dimensional supersymmetry theory with N = 2 supersymmetry. We will analyze the quantization of this theory, in the presence of a boundary. The effective Lagrangian used in the path integral quantization of this theory, will be given by the sum of the gauge fixing term and the ghost term with the original classical Lagrangian. Even though the supersymmetry of this effective Lagrangian will also be broken due to the presence of a boundary, it will be demonstrated that half of the supersymmetry of this theory can be preserved by adding a boundary Lagrangian to the effective bulk Lagrangian. The supersymmetric transformation of this new boundary Lagrangian will exactly cancel the boundary term generated from the supersymmetric transformation of the effective bulk Lagrangian. We will analyze the Slavnov–Taylor identity for this N = 2 Yang–Mills theory with a boundary.

Supersymmetry from boundary conditions

2005

We study breaking and restoration of supersymmetry in five-dimensional theories by determining the mass spectrum of fermions from their equations of motion. Boundary conditions can be obtained from either the action principle by extremizing an appropriate boundary action (interval approach) or by assigning parities to the fields (orbifold approach). In the former, fields extend continuously from the bulk to the boundaries, while in the latter the presence of brane mass-terms cause fields to jump when one moves across the branes. We compare the two approaches and in particular we carefully compute the non-trivial jump profiles of the wavefunctions in the orbifold picture for very general brane mass terms. We also include the effect of the Scherk-Schwarz mechanism in either approach and point out that for a suitable tuning of the boundary actions supersymmetry is present for arbitrary values of the Scherk-Schwarz parameter. As an application of the interval formalism we construct bulk and boundary actions for super Yang-Mills theory. Finally we extend our results to the warped Randall-Sundrum background.

D = 10 supersymmetric Yang-Mills theory at α′4

Journal of High Energy Physics, 2010

The α ′2 deformation of D = 10 SYM is the natural generalisation of the F 4 term in the abelian Born-Infeld theory. It is shown that this deformation can be extended to α ′4 in a way which is consistent with supersymmetry. The latter requires the presence of higher-derivative and commutator terms as well as the symmetrised trace of the Born-Infeld α ′4 term.

N = 1 supersymmetric sigma model with boundaries, II

Nuclear Physics B, 2004

We study an N = 1 two-dimensional non-linear sigma model with boundaries representing, e.g., a gauge fixed open string. We describe the full set of boundary conditions compatible with N = 1 superconformal symmetry. The problem is analyzed in two different ways: by studying requirements for invariance of the action, and by studying the conserved supercurrent. We present the target space interpretation of these results, and identify the appearance of partially integrable almost product structures.

N = 1 Supersymmetric Sigma Model with Boundaries, I

Communications in Mathematical Physics, 2003

Towards the complete N=2 superfield Born-Infeld action with partially broken N=4 supersymmetry

Physical Review D, 2001

We propose a systematic way of constructing N = 2, d = 4 superfield Born-Infeld action with a second nonlinearly realized N = 2 supersymmetry. The latter, together with the manifest N = 2 supersymmetry, form a central-charge extended N = 4, d = 4 supersymmetry. We embed the Goldstone-Maxwell N = 2 multiplet into an infinite-dimensional off-shell supermultiplet of this N = 4 supersymmetry and impose an infinite set of covariant constraints which eliminate all extra N = 2 superfields through the Goldstone-Maxwell one. The Born-Infeld superfield Lagrangian density is one of these composite superfields. The constraints can be solved by iterations to any order in the fields. We present the sought N = 2 Born-Infeld action up to the 10th order. It encompasses the action found earlier by Kuzenko and Theisen to the 8th order from a self-duality requirement. This is a strong indication that the complete N = 2 Born-Infeld action with partially broken N = 4 supersymmetry is also self-dual.

Four-dimensional superconformal theories with interacting boundaries or defects

Physical Review D, 2002

We study four-dimensional superconformal field theories coupled to three-dimensional superconformal boundary or defect degrees of freedom. Starting with bulk N = 2, d = 4 theories, we construct abelian models preserving N = 2, d = 3 supersymmetry and the conformal symmetries under which the boundary/defect is invariant. We write the action, including the bulk terms, in N = 2, d = 3 superspace. Moreover we derive Callan-Symanzik equations for these models using their superconformal transformation properties and show that the beta functions vanish to all orders in perturbation theory, such that the models remain superconformal upon quantization. Furthermore we study a model with N = 4 SU (N ) Yang-Mills theory in the bulk coupled to a N = 4, d = 3 hypermultiplet on a defect. This model was constructed by DeWolfe, Freedman and Ooguri, and conjectured to be conformal based on its relation to an AdS configuration studied by Karch and Randall. We write this model in N = 2, d = 3 superspace, which has the distinct advantage that non-renormalization theorems become transparent. Using N = 4, d = 3 supersymmetry, we argue that the model is conformal.

A Manifestly N=2 Supersymmetric Born–Infeld Action

Modern Physics Letters A, 1999

A manifestly N=2 supersymmetric completion of the four-dimensional Nambu-Goto-Born-Infeld action, which is self-dual with respect to electric-magnetic duality, is constructed in terms of an abelian N=2 superfield strength W in the conventional N=2 superspace. A relation to the known N=1 supersymmetric Born-Infeld action in N=1 superspace is established. The action found can be considered either as the Goldstone action associated with a partial breaking of N=4 supersymmetry down to N=2, with the N=2 vector superfield being a Goldstone field, or, equivalently, as the gauge-fixed superfield action of a D-3-brane in flat six-dimensional ambient spacetime.

BPS-saturated walls in supersymmetric theories

Domain-wall solutions in four-dimensional supersymmetric field theories with distinct discrete vacuum states lead to the spontaneous breaking of supersymmetry, either completely or partially. We consider in detail the case when the domain walls are the BPS-saturated states, and 1/2 of supersymmetry is preserved. Several useful criteria that relate the preservation of 1/2 of supersymmetry on the domain walls to the central extension appearing in the N = 1 superalgebras are established. We explain how the central extension can appear in N = 1 supersymmetry and explicitly obtain the central charge in various models: the generalized Wess-Zumino models, and supersymmetric Yang-Mills theories with or without matter. The BPSsaturated domain walls satisfy the first-order differential equations which we call the creek equations, since they formally coincide with the (complexified) equations of motion of an analog high-viscosity fluid on a profile which is given by the superpotential of the original problem. Some possible applications are considered. We also briefly discuss BPS-saturated strings.

Four dimensional supersymmetric theories in presence of a boundary (original) (raw)

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