We present an explicit calculation of the one-loop quantum corrections to the mass and the two central charges of the kink solution of an N=(2,2) supersymmetric CP^1 model with twisted mass, using supersymmetry preserving dimensional regularization adapted to solitons. We find that the quantum corrections of the mass and one of the central charges are nontrivial (but saturate the BPS bound), while the other central charge receives no corrections. The nontrivial central charge correction corresponds to a quantum anomaly, which in our scheme appears as parity violation in the regulating extra dimension, and its magnitude is in agreement with exact results obtained by Dorey on the basis of a massive analog of mirror symmetry from a dual U(1) gauge theory, confirming also the recent work by Shifman, Vainshtein, and Zwicky.
We present an analytic result for the 1-loop quantum mass correction in semiclassical quantization for the twisted ϕ^4 kink on S^1 without explicit knowledge of the fluctuation spectrum. For this purpose we use the contour integral representation of the spectral zeta function. By solving the Bethe ansatz equations for the n=2 Lame equation we obtain an analytic expression for the corresponding spectral discriminant. We discuss the renormalization issues of this model. An energetically preferred size for the compact space is finally obtained.
We consider quantum corrections to a kink of noncommutative supersymmetric phi^4 theory in 1+1 dimensions. Despite the presence of an infinite number of time derivatives in the action, we are able to define supercharges and a Hamiltonian by using an unconventional canonical formalism. We calculate the quantum energy E of the kink (defined as a half-sum of the eigenfrequencies of fluctuations) which coincides with its' value in corresponding commutative theory independently of the noncommutativity parameter. The renormalization also proceeds precisely as in the commutative case. The vacuum expe…
We show that the anomalous contribution to the central charge of the 1+1-dimensional N=1 supersymmetric kink that is required for BPS saturation at the quantum level can be linked to an analogous term in the extra momentum operator of a 2+1-dimensional kink domain wall with spontaneous parity violation and chiral domain wall fermions. In the quantization of the domain wall, BPS saturation is preserved by nonvanishing quantum corrections to the momentum density in the extra space dimension. Dimensional reduction from 2+1 to 1+1 dimensions preserves the unbroken N=1/2 supersymmetry and turns the…
We apply zeta-function regularization to the kink and susy kink and compute its quantum mass. We fix ambiguities by the renormalization condition that the quantum mass vanishes as one lets the mass gap tend to infinity while keeping scattering data fixed. As an alternative we write the regulated sum over zero point energies in terms of the heat kernel and apply standard heat kernel subtractions. Finally we discuss to what extent these procedures are equivalent to the usual renormalization conditions that tadpoles vanish.
We study a variety of supersymmetric systems describing sixth-order interactions between two coupled real superfields in 2+1 dimensions. We search for BPS domain ribbon solutions describing minimum energy static field configurations that break one half of the supersymmetries. We then use the supersymmetric system to investigate the behavior of mesons and fermions in the background of the defects. In particular, we show that certain BPS domain ribbons admit internal structure in the form of bosonic kinks and fermionic condensate, for a given range of the two parameters that completely identify …
We continue the investigation of supersymmetric extensions of field theories with a non-standard kinetic term (K field theories) resumed recently. Concretely, for K field theories which allow for kink or compacton solutions in 1+1 dimensions, i.e., for domain walls in a higher-dimensional context, we find a simple supersymmetric extension such that the boson field still has the kink solution, and the field equation for the fermion in the kink background is linear and is solved by the first spatial derivative of the kink, as is the case in the corresponding standard supersymmetric theories. Thi…
We consider the N=1 supersymmetric kink on a circle, i.e., on a finite interval with boundary or transition conditions which are locally invisible. For Majorana fermions, the single-particle Dirac Hamiltonian as a differential operator obeys simultaneously the three discrete symmetries of charge conjugation, parity, and time reversal. However, no single locally invisible transition condition can satisfy all three. When calculating sums over zero-point energies by mode number regularization, this gives a new rationale for a previous suggestion that one has to average over different choices of b…
We discuss the one-loop quantum corrections to the mass M and central charge Z of supersymmetric solitons: the kink, the vortex and the monopole. Contrary to previous expectations and published results, in each of these cases there are nonvanishing quantum corrections to the mass. For the N=1 kink and the N=2 monopole a new anomaly in Z rescues BPS saturation (M=Z); for the N=2 vortex, BPS saturation is rescued for two reasons: (i) the quantum fluctuations of the Higgs field acquire a nontrivial phase due to the winding of the classical solution, and (ii) a fermionic zero mode used in the lite…
We discuss the possibility to absorb all anomalies in the supersymmetry algebra of the N=(1,1) Wess-Zumino model in d=1+1 by a local counter term. This counter term corresponds to the change of the vacuum parameter $v_0^2$ in the model and the transition to an unconventional but admissible renormalization scheme. It does not modify the physical consequences such as BPS saturation, and thus the situation is rather different from gauge theory where local counter terms are required to absorb spurious gauge anomalies.
We find the general solution to the time-dependent Hartree-Fock problem for the Gross-Neveu models, with both discrete (GN2) and continuous (NJL2) chiral symmetry. We find new multi-baryon, multi-breather and twisted breather solutions, and show that all GN2 baryons and breathers are composed of constituent twisted kinks of the NJL2 model.
Twisted kinks in the massless NJL$_2$ model interpolate between two distinct vacua on the chiral circle. If one approaches the chiral limit from finite bare fermion masses $m_0$, the vacuum is unique and twist cannot exist. This issue is studied analytically in the non-relativistic limit, using a no-sea effective theory. We conclude that even in the massless limit, the interpretation of the twisted kink has to be revised. One has to attribute the fermion number of the valence state to the twisted kink. Fermion density is spread out over the whole space due to the massless pion field. The resul…
Massive maximally-supersymmetric sigma models are shown to exhibit multiple static kink-domain wall solutions that preserve 1/2 of the supersymmetry. The kink moduli space admits a natural Kahler metric. We examine in some detail the case when the target of the sigma model is given by the co-tangent bundle of CP^n equipped with the Calabi metric, and we show that there exist BPS solutions corresponding to n kinks at arbitrary separation. We also describe how 1/4-BPS charged and intersecting domain walls are described in the low-energy dynamics on the kink moduli space. We comment on the simila…
Holographic superconductor model represents various inhomogeneous solutions with homogeneous sources. In this paper, we study inhomogeneous structures in the presence of the homogeneous current and the chemical potential. We find single complex kink condensates, multiple complex kinks condensates and twisted kink crystal condensates in which both the amplitude and the phase of the order parameter modulate in space. Analyzing the gauge-invariant phase difference in the single complex kink condensates, we find the non-monotonic behaviour with respect to the current. We confirm that the multiple …
We consider domain walls obtained by embedding the 1+1-dimensional $ϕ^4$-kink in higher dimensions. We show that a suitably adapted dimensional regularization method avoids the intricacies found in other regularization schemes in both supersymmetric and non-supersymmetric theories. This method allows us to calculate the one-loop quantum mass of kinks and surface tensions of kink domain walls in a very simple manner, yielding a compact d-dimensional formula which reproduces many of the previous results in the literature. Among the new results is the nontrivial one-loop correction to the surface…
As a consequence of axial current conservation, fermions cannot be localized in the massless NJL$_2$ model. In the case of twisted kinks, this manifests itself in a cancellation between valence fermion density and fermion density induced in the Dirac sea. To attribute the correct fermion number to these bound states requires an infrared regularization. Recently, this has been achieved by introducing a bare fermion mass, at least in the non-relativistic regime of small twist angles and fermion numbers. Here, we propose a simpler regularization by a finite box which preserves integrability and c…
Recently we observed a crossover transition (in the Fayet-Iliopoulos parameter) from weak to strong coupling in N=2 supersymmetric QCD with the U(N) gauge group and N_f > N quark flavors. At strong coupling this theory can be described by a dual non-Abelian weakly coupled SQCD with the dual gauge group U(N_f-N) and N_f light dyon flavors. Both theories support non-Abelian strings. We continue the study of confinement dynamics in these theories, in particular, metamorphoses of excitation spectra, from a different side. A number of results obtained previously are explained, enhanced and suppleme…
The two-dimensional, massless Gross-Neveu model with Nc colors and SU(2) isospin is studied analytically in the large Nc limit. The chiral SU(2)L X SU(2)R symmetry is broken spontaneously in the vacuum. Twisted kinks connecting two arbitrary points on the vacuum manifold S3 are constructed, and their properties are explored. The phase diagram as a function of temperature, baryon- and isospin chemical potential is discussed, with special emphasis on inhomogeneous phases. The preferred form of the condensate is a product of the real kink crystal and the chiral spiral. Kink-kink scattering is sol…
Massive D=4 N=2 supersymmetric sigma models typically admit domain wall (Q-kink) solutions and string (Q-lump) solutions, both preserving 1/2 supersymmetry. We exhibit a new static 1/4 supersymmetric `kink-lump' solution in which a string ends on a wall, and show that it has an effective realization as a BIon of the D=4 super DBI-action. It is also shown to have a time-dependent Q-kink-lump generalization which reduces to the Q-lump in a limit corresponding to infinite BI magnetic field. All these 1/4 supersymmetric sigma-model solitons are shown to be realized in M-theory as calibrated, or `Q…
We review our work on computations of the quantum corrections to the mass and the central charge of the susy kink. For the mass corrections, we find that the widely used momentum cut-off scheme gives an incorrect result, but we deduce through smoothing of the cut-off an extra term in the mass formula, which produces the correct result. We discover the importance of boundary effects for the mode number cut-off regularization scheme. We introduce the notion of delocalized boundary energy. We discuss two discrete $Z_2$ symmetries and their importance to the mode number approach. For the central c…
We study the supersymmetric kink with higher derivative and momentum cut-off regularization schemes. We introduce the new momentum cut-off regularization scheme which we call ``generalized momentum cut-off''. A new, explicit computation for the central charge anomaly for this scheme is described in detail. The calculation of the first order mass corrections for the bosonic and supersymmetric kink within the momentum cut-off is presented in hep-th/0010051, so that one can compare the one-loop central charge and mass computed independently within the same regularization setup. We confirm that th…
Darboux transformations are employed in construction and analysis of Dirac Hamiltonians with pseudoscalar potentials. By this method, we build a four parameter class of reflectionless systems. Their potentials correspond to composition of complex kinks, also known as twisted kinks, that play an important role in the $1+1$ Gross-Neveu and Nambu-Jona-Lasinio field theories. The twisted kinks turn out to be multi-solitonic solutions of the integrable AKNS hierarchy. Consequently, all the spectral properties of the Dirac reflectionless systems are reflected in a non-trivial conserved quantity, whi…
The Gross-Neveu model with ${\rm U}_L(N_f)\times{\rm U}_R(N_f)$ chiral symmetry is reconsidered in the large $N_c$ limit. The known analytical solution for the time dependent interaction of any number of twisted kinks and breathers is cast into a more revealing form. The ($x,t$)-dependent factors are isolated from constant coefficients and twist matrices. These latter generalize the twist phases of the single flavor model. The crucial tool is an identity for the inverse of a sum of two square matrices, derived from the known formula for the determinant of such a sum.
This paper investigates a model containing $ϕ^4$ kinks interacting with fermions. The fermion back-reaction is included in the equations of motion, which affects the kink-antikink collisions. We show that the fermion field generates a force that can be either attractive or repulsive. Moreover, we investigate three different scenarios, which exhibit a wide variety of behaviors including the usual scenarios observed in the $ϕ^4$ model as well as the formation of two oscillons, reflection without contact, one-bounce resonance windows, and the creation of kink-antikink pairs. We also find evidence…
We calculate vacuum energy for twisted SUSY D-brane on toroidal background with constant magnetic or constant electric field. Its behaviour for toroidal D-brane (p=2) in constant electric field shows the presence of stable minimum for twisted versions of the theory. That indicates such a background maybe reasonable groundstate.
Herein, we consider a topologically twisted version of maximally supersymmetric Yang-Mills theory in five dimensions which was introduced by Witten in 2011. We consider this theory on a five manifold of the form M_4 x I for M_4 an oriented Riemannian four manifold. The complete and unique action of the theory in bulk is written down and is shown to be invariant under two scalar supersymmetries.
We study three-dimensional ${\mathcal N}=2$ supersymmetric gauge theories on ${Σ_g \times S^1}$ with a topological twist along $Σ_g$, a genus-$g$ Riemann surface. The twisted supersymmetric index at genus $g$ and the correlation functions of half-BPS loop operators on $S^1$ can be computed exactly by supersymmetric localization. For $g=1$, this gives a simple UV computation of the 3d Witten index. Twisted indices provide us with a clean derivation of the quantum algebra of supersymmetric Wilson loops, for any Yang-Mills-Chern-Simons-matter theory, in terms of the associated Bethe equations for…
Mass perturbations of the twisted N=4 supersymmetric gauge theory considered by Vafa and Witten to test S-duality are studied for the case of Kahler four-manifolds. It is shown that the resulting mass-perturbed theory can be regarded as an equivariant extension associated to a U(1) symmetry of the twisted theory, which is only present for Kahler manifolds. In addition, it is shown that the partition function, the only topological invariant of the theory, remains invariant under the perturbation.
We present the supersymmetric completion of the M-theory free differential algebra resulting from a compactification to four dimensions on a twisted seven-torus with 4-form and 7-form fluxes turned on. The super--curvatures are given and the local supersymmetry transformations derived. Dual formulations of the theory are discussed in connection with classes of gaugings corresponding to diverse choices of vacua. This also includes seven dimensional compactifications on more general spaces not described by group manifolds.
We study aspects of 3d $\mathcal{N}=2$ supersymmetric gauge theories on the product of a line and a Riemann surface. Performing a topological twist along the Riemann surface leads to an effective supersymmetric quantum mechanics on the line. We propose a construction of the space of supersymmetric ground states as a graded vector space in terms of a certain cohomology of generalized vortex moduli spaces on the Riemann surface. This exhibits a rich dependence on deformation parameters compatible with the topological twist, including superpotentials, real mass parameters, and background vector b…
Integrable spin chains in twisted maximally supersymmetric Yang-Mills theory
Instituto Galego de Física de Altas Enerxías (IGFAE) and Departamento de Física de Partículas, Universidade de Santiago de Compostela（加利西亚高能物理研究所和圣地亚哥德孔波斯特拉大学粒子物理系）；Institut für Physik, Humboldt-Universität zu Berlin（柏林洪堡大学物理研究所）
We compute the quantum correction to the mass of the kink at the one-loop level in (1+1) dimensions with minimal supersymmetry. In this paper we discuss this issue from the Casimir energy perspective using phase shifts along with the mode number cut-off regularization method. Exact solutions and in particular an exact expression for the phase shifts are already available for the bosonic sector. In this paper we derive analogous exact results for the fermionic sector. Most importantly, we derive a unique and exact expression for the fermionic phase shift, using the exact solutions for the conti…
In this paper a new version of the DHN (Dashen-Hasslacher-Neveu) formula, which is used to compute the one-loop order kink mass correction in (1+1)-dimensional scalar field theory models, is constructed. The new expression is written in terms of the spectral data coming from the supersymmetric partner operator of the second-order small kink fluctuation operator and allows us to compute the kink mass quantum shift in new models for which this calculation was out of reach by means of the old formula.
We derive the partition function of an $\mathcal N=2$ chiral multiplet on topologically twisted $H^2\times S^1$. The chiral multiplet is coupled to a background vector multiplet encoding a real mass deformation. We consider an $ H^2\times S^1$ metric containing two parameters: one is the $S^1$ radius, while the other gives a fugacity $q$ for the angular momentum on $H^2$. The computation is carried out by means of supersymmetric localization, which provides a finite answer written in terms of $q$-Pochammer symbols and multiple Zeta functions. Especially, the partition function of normalizable …
We propose a quantum simulation of a supersymmetric lattice model using atoms trapped in a 1D configuration and interacting through a Rydberg dressed potential. The elementary excitations in the model are kinks or (in a sector with one extra particle) their superpartners - the skinks. The two are connected by supersymmetry and display identical quantum dynamics. We provide an analytical description of the kink/skink quench dynamics and propose a protocol to prepare and detect these excitations in the quantum simulator. We make a detailed analysis, based on numerical simulation, of the Rydberg …
We consider a twisted version of the four-dimensional N=4 supersymmetric Yang-Mills theory with gauge groups SU(2) and SO(3), and bare masses for two of its chiral multiplets, thereby breaking N=4 down to N=2. Using the wall-crossing technique introduced by Moore and Witten within the u-plane approach to twisted topological field theories, we compute the partition function and all the topological correlation functions for the case of simply-connected spin four-manifolds of simple type. By including 't Hooft fluxes, we analyse the properties of the resulting formulae under duality transformatio…
At one loop, quantum kinks are described by a sum of quantum harmonic oscillator Hamiltonians, and the ground state is just the product of the oscillator ground states. Two-loop kink masses are only known in integrable and supersymmetric cases and two-loop states have never been found. We find the two-loop kink mass and explicitly construct the two-loop kink ground state in a scalar field theory with an arbitrary nonderivative potential. We use a coherent state operator which maps the vacuum sector to the kink sector, allowing all states to be treated with a single Hamiltonian which needs to b…
We present the detailed properties of a self-consistent crystalline chiral condensate in the massless chiral Gross-Neveu model. We show that a suitable ansatz for the Gorkov resolvent reduces the functional gap equation, for the inhomogeneous condensate, to a nonlinear Schrödinger equation, which is exactly soluble. The general crystalline solution includes as special cases all previously known real and complex condensate solutions to the gap equation. Furthermore, the associated Bogoliubov-de Gennes equation is also soluble with this inhomogeneous chiral condensate, and the exact spectral pro…
We present a detailed description of the three inequivalent twists of N=4 supersymmetric gauge theories. The resulting topological quantum field theories are reobtained in the framework of the Mathai-Quillen formalism and the corresponding moduli spaces are analyzed. We study their geometric features in each case. In one of the twists we make contact with the theory of non-abelian monopoles in the adjoint representation of the gauge group. In another twist we obtain a topological quantum field theory which is orientation reversal invariant. For this theory we show how the functional integral c…
Twisted compactification of the 6d N=(2,0) theories on a punctured Riemann surface give a large class of 4d N=1 and N=2 gauge theories, called class S. We argue that nonperturbative dynamics of class S theories are described by 5d maximal Super-Yang-Mills (SYM) twisted on the Riemann surface. In a sense, twisted 5d SYM might be regarded as a "Lagrangian" for class S theories on R^{1,2} times S^1. First, we show that twisted 5d SYM gives generalized Hitchin's equations which was proposed recently. Then, we discuss how to identify chiral operators with quantities in twisted 5d SYM. Mesons, or ho…
The construction of twisted K-theory classes on a compact Lie group is reviewed using the supersymmetric Wess-Zumino-Witten model on a cylinder. The Quillen superconnection is introduced for a family of supercharges and the Chern character for the family is given and its relation to twisted cohomology is discussed.
We study the twisted index of 3d $\mathcal{N}=2$ supersymmetric gauge theories on $S^1 \times Σ$ in the presence of a real FI parameter deformation. This parameter induces a 1d FI parameter for the effective supersymmetric quantum mechanics on $S^1$. Using supersymmetric localisation, the twisted index can be expressed as a contour integral. We show that the contour prescription is modified in the presence of the 1d FI parameter, leading to wall-crossing phenomena for the twisted index. In particular, we derive a general wall-crossing formula for abelian gauge theories. We also examine the ori…
We examine the relation between twisted versions of the extended supersymmetric gauge theories and supersymmetric orbifold lattices. In particular, for the $\mathcal{N}=4$ SYM in $d=4$, we show that the continuum limit of orbifold lattice reproduces the twist introduced by Marcus, and the examples at lower dimensions are usually Blau-Thompson type. The orbifold lattice point group symmetry is a subgroup of the twisted Lorentz group, and the exact supersymmetry of the lattice is indeed the nilpotent scalar supersymmetry of the twisted versions. We also introduce twisting in terms of spin groups…
We present an encompassing treatment of D-brane charges in supersymmetric SO(3) WZW models. There are two distinct supersymmetric CFTs at each even level: the standard bosonic SO(3) modular invariant tensored with free fermions, as well as a novel twisted model. We calculate the relevant twisted K-theories and find complete agreement with the CFT analysis of D-brane charges. The K-theoretical computation in particular elucidates some important aspects of N=1 supersymmetric WZW models on non-simply connected Lie groups.
Non-supersymmetric Yang-Mill gauge theory in 4-dimension is shown to be dual to 4-dimensional non-supersymmetric string theory in a twisted AdS2(n)xT2 spacetime background. The partition function of a generic hadron is calculated to illustrate the mathematical structure of the twisted QCD topology. The physical implications of the twisted QCD topology are discussed.
The vacuum structure and spectra of two-dimensional gauge theories with N=(2,2) supersymmetry are investigated. These theories admit a twisted mass term for charged chiral matter multiplets. In the case of a U(1) gauge theory with N chiral multiplets of equal charge, an exact description of the BPS spectrum is obtained for all values of the twisted masses. The BPS spectrum has two dual descriptions which apply in the Higgs and Coulomb phases of the theory respectively. The two descriptions are related by a massive analog of mirror symmetry: the exact mass formula which is given by a one-loop c…
The present paper deals with N=1 2D supersymmetric integrable quantum field theory. The S-matrix proposed to describe the interactions between supersymmetric particles is applied to theories involving topological excitations of zero central charge. Bound states can fit consistently within this type of theories, since the bootstrap can be shown to close. The topological character of the excitations and the similarity with the scattering of particles is fully understood when a kink sector is introduced in the theory.
We study spectrum of D=2 N=(2,2) QED with N+1 massive charged chiral multiplets, with care given to precise supermultiplet countings. In the infrared the theory flows to CP^N model with twisted masses, where we construct generic flavored kink solitons for the large mass regime, and study their quantum degeneracies. These kinks are qualitatively different and far more numerous than those of small mass regime, with features reminiscent of multi-pronged (p,q) string web, complete with the wall-crossing behavior. It has been also conjectured that spectrum of this theory is equivalent to the hyperm…
We describe special supersymmetric gauge theories in three, five, seven and nine dimensions, whose compactification on two-, four-, six- and eight-folds produces a supersymmetric quantum mechanics on moduli spaces of holomorphic bundles and/or solutions to the analogues of instanton equations in higher dimensions. The theories may occur on the worldvolumes of D-branes wrapping manifolds of special holonomy. We also discuss the theories with matter.
This thesis studies the algebro-geometric aspects of supersymmetric abelian gauge theories in three dimensions. The supersymmetric vacua are demonstrated to exhibit a window phenomenon in Chern-Simons levels, which is analogous to the window phenomenon in quantum K-theory with level structures. This correspondence between three-dimensional gauge theories and quantum K-theory is investigated from the perspectives of semi-classical vacua, twisted chiral rings, and twisted indices. In particular, the twisted index admits an algebro-geometric interpretation as the supersymmetric index of an effect…
Using recent results of the author along with Vander Werf, we present the classification and construction of mirror-twisted modules for N=2 supersymmetric vertex operator superalgebras of the form $V \otimes V$ for the signed transposition mirror map automorphism. In particular, we show that the category of such mirror-twisted sectors for $V\otimes V$ is isomorphic to the category of N=1 Ramond sectors for $V$.
We analyze the dynamics of a general two-dimensional $\mathcal{N}=(2,2)$ gauged linear sigma model with semichiral superfields. By computing the elliptic genera, we study the vacuum structure of the model. The result coincides with the model without using semichiral superfields. We also show that the low energy effective twisted superpotential contributed by semichiral superfields vanishes, whether we turn on twisted masses or not.
In this paper we apply supersymmetric localization to study gauged linear sigma models (GLSMs) describing supermanifold target spaces. We use the localization method to show that A-twisted GLSM correlation functions for certain supermanifolds are equivalent to A-twisted GLSM correlation functions for hypersurfaces in ordinary spaces under certain conditions. We also argue that physical two-sphere partition functions are the same for these two types of target spaces. Therefore, we reproduce the claim of arXiv:hep-th/9404186, arXiv:hep-th/9506070. Furthermore, we explore elliptic genera and (0,2…
Inspired by the tachyon-free non-supersymmetric heterotic SO(16)xSO(16) string we consider a special class of non-supersymmetric field theories: Those that can be obtained from supersymmetric field theories by supersymmetry breaking twists. We argue that such theories, like their supersymmetric counter parts, may still possess some fermionic symmetries as left-overs of the super gauge transformations and have special one-loop non-renormalization properties due to holomorphicity. In addition, we extend the supergraph techniques to these theories to calculate some explicit supersymmetry-breaking…
The construction of twisted K-theory classes on a compact Lie group is reviewed using the supersymmetric Wess-Zumino-Witten model on a cylinder. The Quillen superconnection is introduced for a family of supercharges parametrized by a compact Lie group and the Chern character is explicitly computed in the case of SU(2). For large euclidean time, the character form is localized on a D-brane.
We review some recent developments in the subject of quantum corrections to soliton mass and central charge. We consider in particular approaches which use local densities for these corrections, as first discussed by Hidenaga Yamagishi. We then consider dimensional regularization of the supersymmetric kink in 1+1 dimensions and an extension of this method to a 2+1-dimensional gauge theory with supersymmetric abelian Higgs vortices as the solitons.
