Topological boundary conditions, the BPS bound, and elimination of ambiguities in the quantum mass of solitons

Abstract

We fix the long-standing ambiguity in the 1-loop contribution to the mass of a 1+1-dimensional supersymmetric soliton by adopting a set of boundary conditions which follow from the symmetries of the action and which depend only on the topology of the sector considered, and by invoking a physical principle that ought to hold generally in quantum field theories with a topological sector: for vanishing mass and other dimensionful constants, the vacuum energies in the trivial and topological sectors have to become equal. In the two-dimensional N=1 supersymmetric case we find a result which for the supersymmetric sine-Gordon model agrees with the known exact solution of the S-matrix but seems to violate the BPS bound. We analyze the nontrivial relation between the quantum soliton mass and the quantum BPS bound and find a resolution. For N=2 supersymmetric theories, there are no one-loop corrections to the soliton mass and to the central charge (and also no ambiguities) so that the BPS bound is always saturated. Beyond 1-loop there are no ambiguities in any theory, which we explicitly check by a 2-loop calculation in the sine-Gordon model.

38 pages

References in corpus (1)

• No saturation of the quantum Bogomolnyi bound by two-dimensional supersymmetric solitons

Cited by in corpus (68)

• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Heat kernels and zeta-function regularization for the mass of the supersymmetric kink
• Looking for a Matrix model of ABJM
• Consistent Boundary Conditions for Open Strings
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• Heavy Fermion Stabilization of Solitons in 1+1 Dimensions
• Nonvanishing quantum corrections to the mass and central charge of the N=2 vortex and BPS saturation
• One-loop surface tensions of (supersymmetric) kink domain walls from dimensional regularization
• Quantum fluctuations of Wilson loops from string models
• Generalized Zeta Functions and One-loop Corrections to Quantum Kink Masses
• Quantum corrections to the mass of the supersymmetric vortex
• One-loop correction to classical masses of quantum kink families
• The anomaly in the central charge of the supersymmetric kink from dimensional regularization and reduction
• SUSY sine-Gordon theory as a perturbed conformal field theory and finite size effects
• Mode regularization of the susy sphaleron and kink: zero modes and discrete gauge symmetry
• Two-Loop Scalar Kinks
• Derivative Expansion and Soliton Masses
• A new renormalization approach to the Dirichlet Casimir effect for ϕ^4 theory in (1+1) dimensions
• Local Casimir Energy For Solitons
• The Dirichlet Casimir effect for ${\varphi }^4$ theory in (3+1) dimensions: A new renormalization approach
• Single State Supermultiplet in 1+1 Dimensions
• A new anomalous contribution to the central charge of the N=2 monopole
• One-Loop Quantum Energy Densities of Domain Wall Field Configurations
• Quantum oscillations of self-dual Abrikosov-Nielsen-Olesen vortices
• On a family of (1+1)-dimensional scalar field theory models: kinks, stability, one-loop mass shifts
• Eliminating ambiguities for quantum corrections to strings moving in $Ad{S}_4\times {\mathbb{CP}}^3$
• Quantum Mass and Central Charge of Supersymmetric Monopoles - Anomalies, current renormalization, and surface terms
• Kink Confinement and Supersymmetry
• Quantum-induced interactions in the moduli space of degenerate BPS domain walls
• Spontaneous Symmetry Breaking and Reflectionless Scattering Data
• One-loop kink mass shifts: a computational approach
• An Effective Field Theory for Fractional Quantum Hall Systems near $\nu =5/2$
• Topological anomalies from the path integral measure in superspace
• One loop corrections to the mass of self-dual semi-local planar topological solitons
• Well-Defined Quantum Soliton Masses Without Supersymmetry
• Quantum corrections to the noncommutative kink
• Excited Kinks as Quantum States
• BPS saturation of the N=4 monopole by infinite composite-operator renormalization
• Accelerating Solitons
• One-loop results for kink and domain wall profiles at zero and finite temperature
• Topological-charge anomalies in supersymmetric theories with domain walls
• Clash of discrete symmetries for the supersymmetric kink on a circle
• Cut-Off Kinks
• Boundary Terms in Supergravity and Supersymmetry
• Sphalerons, knots, and dynamical compactification in Yang-Mills-Chern-Simon theories
• Effective Energy Approach to Collectively Quantized Systems
• Bound States of Majorana Fermions in Semi-classical Approximation
• Stability Equation and Two-Component Eigenmode for Domain Walls in a Scalar Potential Model
• Wilson loops from supergravity and string theory
• Quantum aspects of a noncommutative supersymmetric kink
• Central charge and renormalization in supersymmetric theories with vortices
• Correlations around an interface
• Comment on `One Loop Renormalization of Soliton Quantum Mass Corrections in 1+1 Dimensional Scalar Field Theory Models' (Phys. Lett. B542 (2002) 282 [hep-th/0206047])
• One-loop quantum correction to the mass of the supersymmetric Kink in (1 + 1) dimensions using the exact spectra and the phase shifts
• Perturbative Quantum Corrections to the Supersymmetric CP^1 Kink with Twisted Mass
• The Radiative Corrections to the Mass of the Kink Using an Alternative Renormalization Program
• A supersymmetric exotic field theory in (1+1) dimensions. One loop soliton quantum mass corrections
• A note on one-loop soliton quantum mass corrections
• Effect of quantum fluctuations on topological excitations and central charge in supersymmetric theories
• Extended multi-scalar field theories in (1+1) dimensions
• On the nature of the anomalies in the supersymmetric kink
• Quantum gravity and the holographic dark energy cosmology
• Degenerate kinks and kink-instantons in two-dimensional scalar field models with $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry
• One-loop quantum cosmological correction to the gravitational constant using the kink solution in de Sitter universe
• The physics of intersecting thick to thin branes
• Ground States of the ${\varphi }^4$ Double-Well QFT
• Domain Walls, The Extended Superconformal Algebra, and The Supercurrent
• One-loop quantum cosmological correction to the gravitational constant in the closed Friedmann-Robertson-Walker universe