Boundary Supersymmetry Research Articles

Supersymmetric Boundaries of One-Dimensional Phases of Fermions beyond Symmetry-Protected Topological States.

It has recently been demonstrated that protected supersymmetry emerges on the boundaries of one-dimensional intrinsically fermionic symmetry protected trivial (SPT) phases. Here we investigate the boundary supersymmetry of one-dimensional fermionic phases beyond SPT phases. Using the connection between Majorana edge modes and real supercharges, we compute, in terms of the bulk phase invariants, the number of protected boundary supercharges.

Boundary terms and three-point functions: an AdS/CFT puzzle resolved

mathcal{N}=8 superconformal field theories, such as the ABJM theory at Chern-Simons level k = 1 or 2, contain 35 scalar operators {mathcal{O}}_{IJ} with Δ = 1 in the 35v representation of SO(8). The 3-point correlation function of these operators is non-vanishing, and indeed can be calculated non-perturbatively in the field theory. But its AdS4 gravity dual, obtained from gauged mathcal{N}=8 supergravity, has no cubic A3 couplings in its Lagrangian, where AIJ is the bulk dual of {mathcal{O}}_{IJ} . So conventional Witten diagrams cannot furnish the field theory result. We show that the extension of bulk supersymmetry to the AdS4 boundary requires the introduction of a finite A3 counterterm that does provide a perfect match to the 3-point correlator. Boundary supersymmetry also requires infinite counterterms which agree with the method of holographic renormalization. The generating functional of correlation functions of the Δ = 1 operators is the Legendre transform of the on-shell action, and the supersymmetry properties of this functional play a significant role in our treatment.

Supergravity at the boundary of AdS supergravity

We give a general analysis of AdS boundary conditions for spin-$3/2$ Rarita-Schwinger fields and investigate boundary conditions preserving supersymmetry for a graviton multiplet in ${\mathrm{AdS}}_{4}$. Linear Rarita-Schwinger fields in ${\mathrm{AdS}}_{d}$ are shown to admit mixed Dirichlet-Neumann boundary conditions when their mass is in the range $0\ensuremath{\le}|m|<1/2{l}_{\mathrm{AdS}}$. We also demonstrate that mixed boundary conditions are allowed for larger masses when the inner product is ``renormalized'' accordingly with the action. We then use the results obtained for $|m|=1/{l}_{\mathrm{AdS}}$ to explore supersymmetric boundary conditions for $\mathcal{N}=1$ ${\mathrm{AdS}}_{4}$ supergravity in which the metric and Rarita-Schwinger fields are fluctuating at the boundary. We classify boundary conditions that preserve boundary supersymmetry or superconformal symmetry. Under the AdS/CFT dictionary, Neumann boundary conditions in $d=4$ supergravity correspond to gauging the superconformal group of the three-dimensional CFT describing M2-branes, while $\mathcal{N}=1$ supersymmetric mixed boundary conditions couple the CFT to $\mathcal{N}=1$ superconformal topologically massive gravity.

Supersymmetry and electroweak breaking in the interval

Hypermultiplets are considered in the five-dimensional interval where all fields are continuous and the boundary conditions are dynamically obtained from the action principle. The orbifold boundary conditions are obtained as particular cases. We can interpret the Scherk-Schwarz supersymmetry breaking as a misalignment of boundary conditions while a new source of supersymmetry breaking corresponding to a mismatch of different boundary parameters is identified. The latter can be viewed as coming from boundary supersymmetry breaking masses for hyperscalars and the nature of the corresponding supersymmetry breaking parameter is analyzed. For some regions of the parameter space where supersymmetry is broken (either by Scherk-Schwarz boundary conditions or by boundary hyperscalar masses) electroweak symmetry breaking can be triggered at the tree level.

N=1 supersymmetric boundary bootstrap

We investigate the boundary bootstrap programme for finding exact reflection matrices of integrable boundary quantum field theories with N=1 boundary supersymmetry. The bulk S-matrix and the reflection matrix are assumed to take the form S ̂ = S ̃ S , R ̂ = R ̃ R , where S̃ and R̃ are the S-matrix and reflection matrix of some integrable non-supersymmetric boundary theory that is assumed to be known, and S and R describe the mixing of supersymmetric indices. Under the assumption that the bulk particles transform in the kink and boson/fermion representations and the ground state is a singlet we present rules by which the supersymmetry representations and reflection factors for excited boundary bound states can be determined. We apply these rules to the boundary sine-Gordon model, to the boundary a 2 (1) and a 4 (1) affine Toda field theories, to the boundary sinh-Gordon model and to the free particle.

Explicit supersymmetry breaking on boundaries of warped extra dimensions

Explicit supersymmetry breaking is studied in higher-dimensional theories by having boundaries respect only a subgroup of the bulk symmetry. If the boundary symmetry is the maximal subgroup allowed by the boundary conditions imposed on the fields, then the symmetry can be consistently gauged; otherwise gauging leads to an inconsistent theory. In a warped fifth dimension, an explicit breaking of all bulk supersymmetries by the boundaries is found to be inconsistent with gauging; unlike the case of flat 5D, complete supersymmetry breaking by boundary conditions is not consistent with supergravity. Despite this result, the low energy effective theory resulting from boundary supersymmetry breaking becomes consistent in the limit where gravity decouples, and such models are explored in the hope that some way of successfully incorporating gravity can be found. A warped constrained standard model leads to a theory with one Higgs boson with mass expected close to the experimental limit. A unified theory in a warped fifth dimension is studied with boundary breaking of both SU(5) gauge symmetry and supersymmetry. The usual supersymmetric prediction for gauge coupling unification holds even though the TeV spectrum is quite unlike the MSSM. Such a theory may unify matter and Higgs in the same SU(5) hypermultiplet.

N=2 boundary supersymmetry in integrable models and perturbed boundary conformal field theory

Boundary integrable models with N=2 supersymmetry are considered. For the simplest boundary N=2 superconformal minimal model with a Chebyshev bulk perturbation we show explicitly how fermionic boundary degrees of freedom arise naturally in the boundary perturbation in order to maintain integrability and N=2 supersymmetry. A new boundary reflection matrix is obtained for this model and N=2 boundary superalgebra is studied. A factorized scattering theory is proposed for a N=2 supersymmetric extension of the boundary sine-Gordon model with either (i) fermionic or (ii) bosonic and fermionic boundary degrees of freedom. Exact results are obtained for some quantum impurity problems: the boundary scaling Lee–Yang model, a massive deformation of the anisotropic Kondo model at the filling values g=2/(2 n+3) and the boundary Ashkin–Teller model.

Tachyon condensation on orbifolds and McKay correspondence

In this Letter we present a mathematical interpretation of tachyon condensation on (three-dimensional) orbifolds within the framework of boundary string field theory (BSFT). We explicitly show that important parts of decay modes in brane–antibrane systems with N =2 boundary supersymmetry can be interpreted as the McKay correspondence described as complexes. This will give an example of the recent interpretation of D-branes as derived category. We also discuss the N =4 boundary supersymmetry as a more refined structure.