Anomaly and quantum corrections to solitons in two-dimensional theories with minimal supersymmetry

We reexamine the issue of the soliton mass in two-dimensional models with N =1 supersymmetry. The superalgebra has a central extension, and at the classical level the soliton solution preserves 1/2 of supersymmetry which is equivalent to BPS saturation. We prove that the property of BPS saturation, i.e. the equality of the soliton mass to the central charge, remains intact at the quantum level in all orders of the weak coupling expansion. Our key finding is an anomaly in the expression for the central charge. The classical central charge, equal to the jump of the superpotential, is amended by an anomalous term proportional to the second derivative of the superpotential. The anomaly is established by various methods in explicit one-loop calculations. We argue that this one-loop result is not affected by higher orders. We discuss in detail how the impact of the boundary conditions can be untangled from the soliton mass calculation. In particular, the soliton profile and the energy distribution are found at one loop. A "supersymmetry" in the soliton mass calculations in the non-supersymmetric models is observed.Comment: 50 pages, LaTex, 2 figures. The version exactly matching that published in Phys.Rev. D. The most essential addition is a footnote, clarifying multiplet shortenin

Emotion dysregulation, impulsivity and anger rumination in borderline personality disorder: the role of amygdala and insula

© 2023 The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/Borderline Personality Disorder (BPD) is a severe mental disorder, characterized by deficits in emotion regulation, interpersonal dysfunctions, dissociation and impulsivity. Brain abnormalities have been generally explored; however, the specific contribution of different limbic structures to BPD symptomatology is not described. The aim of this study is to cover this gap, exploring functional and structural alterations of amygdala and insula and to highlight their contribution to neuropsychiatric symptoms. Twenty-eight BPD patients (23.7 ± 3.42 years; 6 M/22F) and twenty-eight matched healthy controls underwent a brain MR protocol (1.5 T, including a 3D T1-weighted sequence and resting-state fMRI) and a complete neuropsychiatric assessment. Volumetry, cortical thickness and functional connectivity of amygdala and insula were evaluated, along with correlations with the neuropsychiatric scales. BPD patients showed a lower cortical thickness of the left insula (p = 0.027) that negatively correlated with the Anger Rumination Scale (p = 0.019; r = − 0.450). A focused analysis on female patients showed a significant reduction of right amygdala volumes in BPD (p = 0.037), that correlate with Difficulties in Emotion Regulation Scale (p = 0.031; r = − 0.415), Beck Depression Inventory (p = 0.009; r = − 0.50) and Ruminative Response Scale (p = 0.045; r = − 0.389). Reduced functional connectivity was found in BPD between amygdala and frontal pole, precuneus and temporal pole. This functional connectivity alterations correlated with Anger Rumination Scale (p = .009; r = − 0.491) and Barratt Impulsiveness Scale (p = 0.020; r = − 0.447). Amygdala and insula are altered in BPD patients, and these two limbic structures are implicated in specific neuropsychiatric symptoms, such as difficulty in emotion regulation, depression, anger and depressive rumination.Peer reviewe

Instanton Calculus and Nonperturbative Relations in N=2 Supersymmetric Gauge Theories

Using instanton calculus we check, in the weak coupling region, the nonperturbative relation =i\pi\left(\cf-{a\over 2} {\partial\cf\over\partial a}\right) obtained for a N=2 globally supersymmetric gauge theory. Our computations are performed for instantons of winding number k, up to k=2 and turn out to agree with previous nonperturbative results.Comment: 18 pages, latex file, no figure

The self-dual gauge fields and the domain wall fermion zero modes

A new type of gauge fixing of the Coulomb gauge domain wall fermion system that reduces the fluctuation of the effective running coupling and the effective mass of arbitrary momentum direction including the region outside the cylinder cut region is proposed and tested in the $16^3\times 32\times 16$ gauge configurations of RBC/UKQCD collaboration. The running coupling at the lowest momentum point does not show infrared suppression and compatible with the experimental data extracted from the JLab collaboration. The source of the fluctuation of the effective mass near momentum $p=$0.6GeV region is expected to be due to the domain wall fermion zero modes.Comment: 12 pages 2 figures, extended arguments and references adde

Exact vortex solutions in a CP^N Skyrme-Faddeev type model

We consider a four dimensional field theory with target space being CP^N which constitutes a generalization of the usual Skyrme-Faddeev model defined on CP^1. We show that it possesses an integrable sector presenting an infinite number of local conservation laws, which are associated to the hidden symmetries of the zero curvature representation of the theory in loop space. We construct an infinite class of exact solutions for that integrable submodel where the fields are meromorphic functions of the combinations (x^1+i x^2) and (x^3+x^0) of the Cartesian coordinates of four dimensional Minkowski space-time. Among those solutions we have static vortices and also vortices with waves traveling along them with the speed of light. The energy per unity of length of the vortices show an interesting and intricate interaction among the vortices and waves.Comment: 21 pages, plain latex, no figure

Novel Branches of (0,2) Theories

We show that recently proposed linear sigma models with torsion can be obtained from unconventional branches of conventional gauge theories. This observation puts models with log interactions on firm footing. If non-anomalous multiplets are integrated out, the resulting low-energy theory involves log interactions of neutral fields. For these cases, we find a sigma model geometry which is both non-toric and includes brane sources. These are heterotic sigma models with branes. Surprisingly, there are massive models with compact complex non-Kahler target spaces, which include brane/anti-brane sources. The simplest conformal models describe wrapped heterotic NS5-branes. We present examples of both types.Comment: 36 pages, LaTeX, 2 figures; typo in Appendix fixed; references added and additional minor change

Nonperturbative SUSY Correlators at Finite Temperature

We calculate finite temperature effects on a correlation function in the two dimensional supersymmetric nonlinear O(3) sigma model. The correlation function violates chiral symmetry and at zero temperature it has been shown to be a constant, which gives rise to a double-valued condensate. Within the bilinear approximation we find an exact result in a one-instanton background at finite temperature. In contrast to the result at zero temperature we find that the correlation function decays exponentially at large distances.Comment: Latex, 27 pages, 1 Postscript figur

Topology in 2D CP**(N-1) models on the lattice: a critical comparison of different cooling techniques

Two-dimensional CP**(N-1) models are used to compare the behavior of different cooling techniques on the lattice. Cooling is one of the most frequently used tools to study on the lattice the topological properties of the vacuum of a field theory. We show that different cooling methods behave in an equivalent way. To see this we apply the cooling methods on classical instantonic configurations and on configurations of the thermal equilibrium ensemble. We also calculate the topological susceptibility by using the cooling technique.Comment: 24 pages, 10 figures (from 16 eps files

Interlayer Exchange Interactions, SU(4) Soft Waves and Skyrmions in Bilayer Quantum Hall Ferromagnets

The Coulomb exchange interaction is the driving force for quantum coherence in quantum Hall systems. We construct a microscopic Landau-site Hamiltonian for the exchange interaction in bilayer quantum Hall ferromagnets, which is characterized by the SU(4) isospin structure. By taking a continuous limit, the Hamiltonian gives rise to the SU(4) nonlinear sigma model in the von-Neumann-lattice formulation. The ground-state energy is evaluated at filling factors $\nu =1,2,3,4$. It is shown at $\nu =1$ that there are 3 independent soft waves, where only one soft wave is responsible for the coherent tunneling of electrons between the two layers. It is also shown at $\nu =1$ that there are 3 independent skyrmion states apart from the translational degree of freedom. They are CP$^{3}$ skyrmions enjoying the spin-charge entanglement confined within the \LLL.Comment: 12 pages, 2 figure

Axion monodromy in a model of holographic gluodynamics

The low energy field theory for N type IIA D4-branes at strong 't Hooft coupling, wrapped on a circle with antiperiodic boundary conditions for fermions, is known to have a vacuum energy which depends on the $\theta$ angle for the gauge fields, and which is a multivalued function of this angle. This gives a field-theoretic realization of "axion monodromy" for a nondynamical axion. We construct the supergravity solution dual to the field theory in the metastable state which is the adiabatic continuation of the vacuum to large values of $\theta$. We compute the energy of this state and show that it initially rises quadratically and then flattens out. We show that the glueball mass decreases with $\theta$, becoming much lower than the 5d KK scale governing the UV completion of this model. We construct two different classes of domain walls interpolating between adjacent vacua. We identify a number of instability modes -- nucleation of domain walls, bulk Casimir forces, and condensation of tachyonic winding modes in the bulk -- which indicate that the metastable branch eventually becomes unstable. Finally, we discuss two phenomena which can arise when the axion is dynamical; axion-driven inflation, and axion strings.Comment: 43 pages, 10 figures. v2: references update