Supersymmetric Inhomogeneous Field Theories in 1+1 Dimensions

Abstract

We study supersymmetric inhomogeneous field theories in 1+1 dimensions which have explicit coordinate dependence. Although translation symmetry is broken, part of supersymmetries can be maintained. In this paper, we consider the simplest inhomogeneous theories with one real scalar field, which possess an unbroken supersymmetry. The energy is bounded from below by the topological charge which is not necessarily nonnegative definite. The bound is saturated if the first-order Bogomolny equation is satisfied. Non-constant static supersymmetric solutions above the vacuum involve in general a zero mode although the system lacks translation invariance. We consider two inhomogeneous theories obtained by deforming supersymmetric sine-Gordon theory and ${\varphi }^6$ theory. They are deformed either by overall inhomogeneous rescaling of the superpotential or by inhomogeneous deformation of the vacuum expectation value. We construct explicitly the most general supersymmetric solutions and obtain the BPS energy spectrum for arbitrary position-dependent deformations. Nature of the solutions and their energies depend only on the boundary values of the inhomogeneous functions. The vacuum of minimum energy is not necessarily a constant configuration. In some cases, we find a one-parameter family of degenerate solutions which include a non-vacuum constant solution as a special case.

arXiv comment29 pages, 5 figures, minor corrections, version published in JHEP

References in corpus (33)

• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Janus Configurations, Chern-Simons Couplings, And The Theta-Angle in N=4 Super Yang-Mills Theory
• Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus
• A Dilatonic Deformation of AdS_5 and its Field Theory Dual
• Interface Yang-Mills, Supersymmetry, and Janus
• Super Janus
• Classically integrable field theories with defects
• Long-range interactions of kinks
• Spectral Walls in Soliton Collisions
• Successive phase transitions and kink solutions in ${\varphi }^8$, ${\varphi }^{10}$, and ${\varphi }^{12}$ field theories
• Vortices and Impurities
• Scattering of the double sine-Gordon kinks
• From Defects to Boundaries
• The ${\varphi }^4$ model with the BPS preserving defect
• Solvable self-dual impurity models
• Supersymmetric extension of the sine-Gordon theory with integrable boundary interactions
• The boundary supersymmetric sine-Gordon model revisited
• BPS soliton-impurity models and supersymmetry
• Janus and Multifaced Supersymmetric Theories
• The BPS property and its breaking in 1+1 dimensions
• Supersymmetric Defect Models and Mirror Symmetry
• Janus and Multifaced Supersymmetric Theories II
• Classical Integrable Super sinh-Gordon equation with defects
• Spatially modulated and supersymmetric deformations of ABJM theory
• Spatially modulated and supersymmetric mass deformations of $\mathcal{N}=4$ SYM
• Integrablility of a Classical $N=2$ Super Sinh-Gordon Model with Jump Defects
• Susy Q and spatially modulated deformations of ABJM theory
• Iterated ${\varphi }^4$ Kinks
• Superconformal RG interfaces in holography
• AdS Q-Soliton and Inhomogeneously mass-deformed ABJM Model
• Thermodynamics of Inhomogeneously Mass-deformed ABJM Model and Pressure Anisotropy
• Domain walls that do not get stuck on impurities
• Super Yang-Mills Theories with Inhomogeneous Mass Deformations

Cited by in corpus (1)

• Spectral Walls at One Loop