We consider limits of $\mathcal{N} = 4$ super-Yang-Mills (SYM) theory that approach BPS bounds. These limits result in non-relativistic near-BPS theories that describe the effective dynamics near the BPS bounds and upon quantization are known as Spin Matrix theories. The near-BPS theories can be obtained by reducing $\mathcal{N}=4$ SYM on a three-sphere and integrating out the fields that become non-dynamical in the limits. We perform the sphere reduction for the near-BPS limit with $\mathrm{SU}(1,2|2)$ symmetry, which has several new features compared to the previously considered cases with $\mathrm{SU}(1,1)$ symmetry, including a dynamical gauge field. We discover a new structure in the classical limit of the interaction term. We show that the interaction term is built from certain blocks that comprise an irreducible representation of the $\mathrm{SU}(1,2|2)$ algebra. Moreover, the full interaction term can be interpreted as a norm in the linear space of this representation, explaining its features including the positive definiteness. This means one can think of the interaction term as a distance squared from saturating the BPS bound. The $\mathrm{SU}(1,1|1)$ near-BPS theory, and its subcases, is seen to inherit these features. These observations point to a way to solve the strong coupling dynamics of these near-BPS theories.
We compute supersymmetric indices which count local operators at certain half-BPS interfaces and quarter-BPS junctions of interfaces in four-dimensional $\mathcal{N}=4$ Super Yang-Mills theory. We use the indices as very stringent tests of a variety of string theory-inspired conjectures about the action of S-duality on such defects.
We consider limits of $\mathcal{N}=4$ super Yang-Mills (SYM) theory that approach BPS bounds and for which an $SU(1,1)$ structure is preserved. The resulting near-BPS theories become non-relativistic, with a $U(1)$ symmetry emerging in the limit that implies the conservation of particle number. They are obtained by reducing $\mathcal{N}=4$ SYM on a three-sphere and subsequently integrating out fields that become non-dynamical as the bounds are approached. Upon quantization, and taking into account normal-ordering, they are consistent with taking the appropriate limits of the dilatation operato…
We consider limits of $\mathcal{N} = 4$ super-Yang-Mills (SYM) theory that approach BPS bounds. These limits result in non-relativistic theories that describe the effective dynamics near the BPS bounds and upon quantization are known as Spin Matrix Theories. The near-BPS theories can be obtained by reducing $\mathcal{N}=4$ SYM on a three-sphere and integrating out the fields that become non-dynamical in the limits. In previous works we have considered various SU(1,1) and SU(1,2) types of subsectors in this limit. In the current work, we will construct the remaining Spin Matrix Theories defined…
We construct non-BPS dyon solutions of N=4 SU(n) supersymmetric Yang-Mills theory. These solutions are the worldvolume solitons which describe non-BPS Type IIB non-planar string junctions connecting n parallel D3-branes. The solutions are smooth deformations of the 1/4 BPS states which describe planar string junctions.
We investigate BPS solutions in ABJM theory on RxS^2. We find new BPS solutions, which have nonzero angular momentum as well as nontrivial configurations of fluxes. Applying the "Higgsing procedure" of arxiv:0803.3218 around a 1/2-BPS solution of ABJM theory, one obtains N=8 super Yang-Mills (SYM) on RxS^2. We also show that other BPS solutions of the SYM can be obtained from BPS solutions of ABJM theory by this higgsing procedure.
We construct BPS saturated regular configurations of N=4 SU(3) supersymmetric Yang-Mills theory carrying non-parallel electric and magnetic charges. These field theory BPS states correspond to the string theory BPS states of 3-string junctions connecting three different D3-branes by regarding the N=4 supersymmetric Yang-Mills theory as an effective field theory on parallel D3-branes.
We consider 10-dimensional super Yang-Mills theory with topological terms compactified on a noncommutative torus. We calculate supersymmetry algebra and derive BPS energy spectra from it. The cases of d-dimensional tori with d=2,3,4 are considered in full detail. SO(d,d|Z)-invariance of the BPS spectrum and relation of new results to the previous work in this direction are discussed.
We construct the classical configurations of BPS states with 1/4 unbroken supersymmetries in four-dimensional N=4 SU(n+1) supersymmetric Yang-Mills theory, and discuss that these configurations correspond to string networks connecting (n+1) D3-branes in Type IIB string theory.
We study supersymmetry of N=4 super Yang-Mills theory in four dimensions deformed in the Omega-background. We take the Nekrasov-Shatashvili limit of the background so that two-dimensional super Poincare symmetry is recovered. We compute the deformed central charge of the superalgebra and study the 1/2 and 1/4 BPS states. We obtain the Omega-deformed 1/2 and 1/4 BPS dyon equations from the deformed supersymmetry transformation and the Bogomol'nyi completion of the energy.
Domain walls in N=1 supersymmetric Yang-Mills theory conjecturally support topological degrees of freedom at low energy. Domain wall junctions are thus expected to support gapless degrees of freedom. We propose a natural candidate for the low-energy description of such junctions.
Extending our previous work on SU(3), we construct spherically symmetric BPS saturated regular configurations of N=4 SU(N) supersymmetric Yang-Mills theory preserving 1/4 supersymmetry, and investigate their features. We also give exact solutions in the case some of the free parameters of the general solutions take certain values. These field theory BPS states correspond to the string theory BPS states of multi-pronged strings connecting N different D3-branes by regarding the N=4 supersymmetric Yang-Mills theory as an effective field theory on parallel D3-branes. We compare our solutions with …
We provide an explicit construction of 1/4 BPS states in four-dimensional N=4 Super-Yang-Mills theory with a gauge group SU(3). These states correspond to three-pronged strings connecting three D3-branes. We also find curves of marginal stability in the moduli space of the theory, at which the above states can decay into two 1/2 BPS states.
We extend the recent conjecture on the relation between a certain 1/8 BPS subsector of 4d N=4 SYM on S^2 and 2d Yang-Mills theory by turning on circular 1/2 BPS 't Hooft operators linked with S^2. We show that localization predicts that these 't Hooft operators and their correlation functions with Wilson operators on S^2 are captured by instanton contributions to the partition function of the 2d Yang-Mills theory. Based on this prediction, we compute explicitly correlation functions involving the 't Hooft operator, and observe precise agreement with S-duality predictions.
It is shown that the BPS spectrum of Super-Yang-Mills theory on $T^d\times \R$, which fits into representations of the U-duality group for M-theory compactified on $T^{d}$, in accordance with the matrix-theory conjecture, in fact fits into representations of the U-duality group for M-theory on $T^{d+1}$, the extra dualities realised as generalised Nahm transformations. The spectrum of BPS M-branes is analysed, new branes are discussed and matrix theory applications described.
We perform a systematic analysis on supersymmetric states in N=4 supersymmetric Yang-Mills theory (SYM) on R x S^3. We find a new set of 1/16 BPS equations and determine the precise configuration of the supersymmetric states by solving all 1/16 BPS equations when they are valued in Cartan subalgebra of a gauge group and the fermionic fields vanish. We also determine the number of supersymmetries preserved by the supersymmetric states varying the parameters of the BPS solutions. As a byproduct we present the complete set of such supersymmetric states in N=8 SYM on R x S^2 by carrying out dimens…
We study singular time-dependent $\frac{1}{8}$-BPS configurations in the abelian sector of ${{\mathcal N}= 4}$ supersymmetric Yang-Mills theory that represent BPS string-like defects in ${{\mathbb R}\times S^3}$ spacetime. Such BPS strings can be described as intersections of the zeros of holomorphic functions in two complex variables with a 3-sphere. We argue that these BPS strings map to $\frac{1}{8}$-BPS surface operators under the state-operator correspondence of the CFT. We show that the string defects are holographically dual to noncompact probe D3-branes in global $AdS_5\times S^5$ that…
We systematically classify 1/2, 1/4 and 1/8 BPS equations in SUSY gauge theories in d=6, 5, 4, 3 and 2 with eight supercharges, with gauge groups and matter contents being arbitrary. Instantons (strings) and vortices (3-branes) are only allowed 1/2 BPS solitons in d=6 with N=1 SUSY. We find two 1/4 BPS equations and the unique 1/8 BPS equation in d=6 by considering configurations made of these field theory branes. All known BPS equations are rederived while several new 1/4 and 1/8 BPS equations are found in dimension less than six by dimensional reductions.
We introduce some techniques for making a more global analysis of the existence of geodesics on a Seiberg-Witten Riemann surface with metric $ds^2 = |λ_{SW}|^2$. Because the existence of such geodesics implies the existence of BPS states in N=2 supersymmetric Yang-Mills theory, one can use these methods to study the BPS spectrum in various phases of the Yang-Mills theory. By way of illustration, we show how, using our new methods, one can easily recover the known results for the N=2 supersymmetric SU(2) pure gauge theory, and we show in detail how it also works for the N=2, SU(2) theory couple…
We show that ${\cal N} = 4$ supersymmetric-Yang-Mills (SYM) theory on $\mathbb{R} \times S^3$ with gauge group $\text{SU}(N)$ is described in a near-BPS limit by a simple lower-dimensional nonrelativistic field theory with $\text{SU}(1,1) \times \text{U}(1)$ invariant interactions. In this limit, a single complex adjoint scalar field survives, and part of its interaction is obtained by exactly integrating out the gauge boson of the SYM theory. Taking into account normal ordering, the interactions match the one-loop dilatation operator of the $\text{SU}(1,1)$ sector, establishing the consistenc…
We start a systematic study of quarter-BPS operators in four-dimensional $\mathcal{N}=4$ Super Yang-Mills with gauge group $\mathrm{SU}(N)$ making use of recently developed tools in conformal field theory. We adapt the technology of embedding space tensor structures in four dimensions to the problem of computing R-symmetry tensor structures and we use the underlying chiral algebra to obtain the superconformal Ward identities. This allows us to fix the protected part of the four-point correlators, up to few ambiguities. As applications, we use the Lorentzian inversion formula to study the leadi…
We determine the low energy dynamics of monopoles in pure N=2 Yang-Mills theories for points in the vacuum moduli space where the two Higgs fields are not aligned. The dynamics is governed by a supersymmetric quantum mechanics with potential terms and four real supercharges. The corresponding superalgebra contains a central charge but nevertheless supersymmetric states preserve all four supercharges. The central charge depends on the sign of the electric charges and consequently so does the BPS spectrum. We focus on the SU(3) case where certain BPS states are realised as zero-modes of a Dirac …
We discuss BPS states preserving 1/4 supersymmetries of N=4 supersymmetric Yang-Mills theory as M2-branes holomorphically embedded and ending on M5-branes. We use techniques in electrodynamics to find the M2-brane configurations, and give some explicit examples. In case the M2-brane worldsheet has handles, the worldsheet moduli of the M2-brane is constrained in a discrete manner. Several aspects of multi-pronged strings in type IIB string theory are beautifully reproduced in the M-theory description. We also discuss the relation between the above construction and the D2-brane dynamics in type …
We apply the BPS Lagrangian method~\cite{Atmaja:2015umo} to derive BPS equations of monopole and dyon in the $SU(2)$ Yang-Mills-Higgs model, Nakamula-Shiraishi models, and their Generalized versions. We argue that by identifying the effective fields of scalar field, $f$, and of time-component gauge field, $j$, explicitly by $j=βf$ with $β$ is a real constant, the usual BPS equations for dyon can be obtained naturally. We validate this identification by showing that both Euler-Lagrange equations for $f$ and $j$ are identical in the BPS limit. The value of $β$ is bounded to $|β|<1$ due to realit…
We study the low-energy effective Hamiltonian of N=2 super Yang-Mills theories. We find that the BPS equations are unchanged outside a quantum core where higher dimension contributions are expected to be important. We find two quantum generalizations of the BPS soliton. The leading higher-derivative correction to the effective action is shown not to contribute to the BPS mass formula.
We systematically classify all possible Bogomol'nyi-Prasad-Sommerfield (BPS) equations in Euclidean dimension $d\leq8$. We discuss symmetries of BPS equations and their connection with the self-dual Yang-Mills equations. Also, we present a general method allowing to obtain the BPS equations in any dimension. In addition, we find all BPS equations in the Minkowski space of dimension $d\leq6$ and apply the obtained results to the supersymmetric Yang-Mills theories. In conclusion, we discuss the possibility of using the classification to construct soliton solutions of the low-energy effective the…
The question of whether BPS invariants are protected in maximally supersymmetric Yang-Mills theories is investigated from the point of view of algebraic renormalisation theory. The protected invariants are those whose cohomology type differs from that of the action. It is confirmed that one-half BPS invariants ($F^4$) are indeed protected while the double-trace one-quarter BPS invariant ($d^2F^4$) is not protected at two loops in D=7, but is protected at three loops in D=6 in agreement with recent calculations. Non-BPS invariants, i.e. full superspace integrals, are also shown to be unprotecte…
We localize the four-dimensional N=4 super Yang-Mills theory on a four-sphere to the two-dimensional constrained Hitchin/Higgs-Yang-Mills (cHYM) theory on a two-sphere S^2. We show that expectation values of certain 1/8 BPS supersymmetric Wilson loops on S^2 in the 4d N=4 SYM is captured by the 2d cHYM theory. We further argue that expectation values of Wilson loops in the cHYM theory agree with the prescription "two-dimensional bosonic Yang-Mills excluding instanton contributions". Hence, we support the recent conjecture by Drukker, Giombi, Ricci and Trancanelli on the 1/8 BPS Wilson loops on…
Two families of SO(2n) Higgs models in $2n$ dimensional spacetime are presented. One family arises from the {\it dimensional reduction} of higher dimensional Yang-Mills systems while the construction of the other one is {\it ad hoc}, the $n=2$ member of each family coinciding with the usual SU(2) Yang-Mills--Higgs system without Higgs potential. All models support BPS 'monopole' solutions. The 'dyons' of the {\it dimensionally descended} models are also BPS, while the electrically charged solutions of the {\it ad hoc} models are not BPS.
We consider N = 4 Yang-Mills theory on a flat four-torus with the R-symmetry current coupled to a flat background connection. The partition function depends on the coupling constant of the theory, but when it is expanded in a power series in the R-symmetry connection around the loci at which one of the supersymmetries is unbroken, the constant and linear terms are in fact independent of the coupling constant and can be computed at weak coupling for all non-trivial 't Hooft fluxes. The case of a trivial 't Hooft flux is difficult because of infrared problems, but the corresponding terms in the …
Procedure of finding of the Bogomolny-Prasad-Sommerfield monopole solutions in the Georgi-Glashow model is investigated in detail on the backgrounds of three space models of constant curvature: Euclid, Riemann, Lobachevski's. Classification of possible solutions is given. It is shown that among all solutions there exist just three ones which reasonably and in a one-to-one correspondence can be associated with respective geometries. It is pointed out that the known non-singular BPS-solution in the flat Minkowski space can be understood as a result of somewhat artificial combining the Minkowski …
We investigate the vacuum structure of pure SU(N) N=1 super Yang-Mills. The theory is expected to possess N vacua with associated domain walls. We show that the newly extended version of the low energy effective Lagrangian for super Yang-Mills supports the BPS domain wall solutions associated with any two vacua aligned with the origin of the moduli space. For the two color theory the domain wall analysis is complete. We also find new non BPS domain wall solutions connecting any two vacua of the underling SU(N) super Yang-Mills theory not necessarely aligned. When two vacua are aligned with the…
We compute form factors of half-BPS operators in N=4 super Yang-Mills dual to massive Kaluza-Klein modes in supergravity. These are appropriate supersymmetrisations T_k of the scalar operators Tr(ϕ^k) for any k, which for k=2 give the chiral part of the stress-tensor multiplet operator. Using harmonic superspace, we derive simple Ward identities for these form factors, which we then compute perturbatively at tree level and one loop. We propose a novel on-shell recursion relation which links form factors with different numbers of fields. Using this, we conjecture a general formula for the n-poi…
Matrix string theory (or more generally U-Duality) requires Super Yang-Mills theory to reflect a stringy degeneracy of BPS short multiplets. These are found as supersymmetric states in the Yang-Mills carrying (fractionated) momentum, or in some cases, instanton number. Their energies also agree with those expected from M(atrix) theory. A nice parallel also emerges in the relevant cases, between momentum and instanton number, (both integral as well as fractional) providing evidence for a recent conjecture relating the two.
We give an explicit expression for classical 1/4-BPS fields in supersymmetric Yang-Mills theory on noncommutative tori. We use it to study quantum 1/4-BPS states. In particular we calculate the degeneracy of 1/4-BPS energy levels.
We study Aharony-Bergman-Jafferis-Maldacena (ABJM) theory without and with mass deformation. It is shown that maximally supersymmetry preserving, D-term, and F-term mass deformations of single mass parameter are equivalent. We obtain vortex-type half-BPS equations and the corresponding energy bound. For the undeformed ABJM theory, the resulting half-BPS equation is the same as that in supersymmetric Yang-Mills theory and no finite energy regular BPS solution is found. For the mass-deformed ABJM theory, the half-BPS equations for U(2)xU(2) case reduce to the vortex equation in Maxwell-Higgs the…
BPS states in N=4 supersymmetric SU(N) gauge theories in four dimensions can be represented as planar string networks with ends lying on D3-branes. We introduce several protected indices which capture information on the spectrum and various quantum numbers of these states, give their wall crossing formula and describe how using the wall crossing formula we can compute all the indices at all points in the moduli space.
We provide a closed-form expression for the motivic Kontsevich-Soibelman invariant for M-theory in the background of the toric Calabi-Yau threefold $K_{\mathbb{F}_0}$. This encodes the refined BPS spectrum of $SU(2)$ 5d ${\cal N}=1$ Yang-Mills theory on $S^1\times \mathbb{R}^4$, corresponding to rank-zero Donaldson-Thomas invariants for $K_{\mathbb{F}_0}$, anywhere on the Coulomb branch.
We construct non-BPS regular and black hole solutions of N=4 SU(N) supersymmetric Yang-Mills theory coupled to Einstein gravity. Our numerical studies reveal a number of interesting phenomena when the gravitational constant $α=M_{YM}/gM_{Planck}$ (where $M_{Planck}$ is the Planck mass and $M_{YM}$ is the monopole mass) is either weak (flat limit) or comparable to the Yang-Mills interaction. In fact, black hole solutions exist in a certain bounded domain in the $(α, r_H)$ plane where $r_H$ denotes the radius of the black
We test the AdS/CFT correspondence by calculating Wilson loops in N = 4 super Yang-Mills theory on R*S^3 in the planar limit. Our method is based on a novel large-N reduction, which reduces the problem to Monte Carlo calculations in the plane-wave matrix model or the BMN matrix model, which is a 1d gauge theory with 16 supercharges. By using the gauge-fixed momentumspace simulation, we obtain results respecting 16 supersymmetries. We report on the Monte Carlo results for the BPS circular Wilson loop, which reproduce the exact result up to strong coupling. As a future prospect, we calculate a t…
We calculate, using noncommutative supersymmetric Yang-Mills gauge theory, the part of the spectrum of the toroidally compactified Matrix theory which corresponds to quantized electric fluxes.
We propose that, in N=4 Super Yang-Mills theory, correlation functions of certain 1/8 BPS Wilson loops and local operators inserted on a S^2 in space-time may be computed in terms of analogous observables in the "zero-instanton" sector of 2d Yang-Mills theory. The Wilson loops are mapped to the standard Wilson loops of the 2d theory, as recently conjectured, while the local operators are mapped to powers of the 2d field strength. We give several perturbative checks of the correspondence, and derive from 2d Yang-Mills a two-matrix model for the correlator of a local operator and a Wilson loop o…
We explore BPS soliton configurations in N=2 supersymmetric Yang-Mills theory with matter fields arising from parallel D3 branes on D7 branes. Especially we focus on two parameter family of 1/8 BPS equations, dyonic objects, and 1/8 BPS objects and raise a possibility of absence of BPS vortices when the number of D3 branes is larger than that of D7 branes.
We investigate the D0-D4-brane system for different B-field backgrounds including the small instanton singularity in noncommutative SYM theory. We discuss the excitation spectrum of the unstable state as well as for the BPS D0-D4 bound state. We compute the tachyon potential which reproduces the complete mass defect. The relevant degrees of freedom are the massless (4,4) strings. Both results are in contrast with existing string field theory calculations. The excitation spectrum of the small instanton is found to be equal to the excitation spectrum of the fluxon solution on R^2_theta x R which…
We derive the central charge and BPS equations from the low-energy effective action for N=2 SU(2) Yang-Mills theory in the Coulomb phase, using a systematic, canonical procedure. We then obtain solutions for monopole and dyon BPS states, whose core structure is described by a dual Lagrangian containing the monopole or dyon as a fundamental field. Spherically symmetric states possess a shell of charge at a characteristic radius.
We study at perturbative level the correlation functions of a general class of 1/8 BPS Wilson loops and chiral primaries in N = 4 Super Yang-Mills theory. The contours and the location of operator insertions share a sphere S^2 embedded into spacetime and the system preserves at least two supercharges. We perform explicit two-loop computations, for some particular but still rather general configuration, that confirm the elegant results expected from localization procedure. We find notably full consistency with the multi-matrix model averages, obtained from 2D Yang-Mills theory on the sphere, wh…
We consider dimensionally reduced three-dimensional supersymmetric Yang-Mills-Chern-Simons theory. Although the N=1 supersymmetry of this theory does not allow true massive Bogomol'nyi-Prasad-Sommerfield (BPS) states, we find approximate BPS states which have non-zero masses that are almost independent of the Yang-Mills coupling constant and which are a reflection of the massless BPS states of the underlying N=1 super Yang-Mills theory. The masses of these states at large Yang-Mills coupling are exactly at the n-particle continuum thresholds. This leads to a relation between their masses at ze…
For N>2 we present static monopole solutions of the second order SU(N) BPS Yang-Mills-Higgs equations which are not solutions of the first order Bogomolny equations. These spherically symmetric solutions may be interpreted as monopole anti-monopole configurations and their construction involves harmonic maps into complex projective spaces.
We study domain walls in two different extensions of super Yang--Mills characterized by the absence of a logarithmic term in their effective superpotential. The models, defined by the usual gaugino condensate and an extra field Y, give different patterns of domain walls despite both leading to the same effective limit for heavy Y, i.e. the Veneziano--Yankielowicz effective Lagrangian of super Yang--Mills. We explain the origin of those differences and also give a physical motivation for introducing the field Y.
BPS representations of 5-dimensional supersymmetry algebras are classified. For BPS states preserving 1/2 the supersymmetry, there are two distinct classes of multiplets for N=4 supersymmetry and three classes for N=8 supersymmetry. For N=4 matter theories, the two 1/2 supersymmetric BPS multiplets are the massive vector multiplet and the massive self-dual 2-form multiplet. Some applications to super-Yang-Mills, supergravity and little string theories are considered.
The free field partition function for a generic U(N) gauge theory, where the fundamental fields transform in the adjoint representation, is analysed in terms of symmetric polynomial techniques. It is shown by these means how this is related to the cycle polynomial for the symmetric group and how the large N result may be easily recovered. Higher order corrections for finite N are also discussed in terms of symmetric group characters. For finite N, the partition function involving a single bosonic fundamental field is recovered and explicit counting of multi-trace quarter BPS operators in free …
The one-instanton contribution to a circular BPS Wilson loop in N=4 SU(2) Yang--Mills theory is evaluated in semiclassical approximation. This article amplifies part of a talk given by MBG at the Strings 2001 conference, Mumbai, India (January 5-10, 2001). The results are preliminary and a more complete exposition will be contained in a forthcoming paper.
The BPS bound is formulated in light-cone superspace for the N = 4 superYang-Mills theory. As a consequence of the superalgebra all momenta are shown to be expressed as a quadratic form in the relevant supertransformations, and these forms are used to derive the light-cone superspace BPS equations. Finally, the superfield expressions are expanded out to component form, and the Wu-Yang Monopole boosted to the infinite momentum frame is shown to be a solution.
We show that Z(N) string's BPS equations are equivalent to the Hitchin's equations (or self-duality equation) and also to the zero curvature condition. We construct a general form for BPS Z(N) string solutions for arbitrary simple gauge groups with non-trivial center. Depending on the vacuum solutions considered, the Z(N) string's BPS equations reduce to different two dimensional integrable field equations. For a particular vacuum we obtain the equation of affine Toda field theory.
We use the well-known Bogomolny's equations, in general coordinate system, for BPS monopoles and dyons in the $SU(2)$ Yang-Mills-Higgs model to obtain an explicit form of BPS Lagrangian density under the BPS Lagrangian method. We then generalize this BPS Lagrangian density and use it to derive several possible generalized Bogomolny's equations, with(out) additional constraint equations, for BPS monopoles and dyons in the generalized $SU(2)$ Yang-Mills-Higgs model. We also compute the stress-energy-momentum tensor of the generalized model, and argue that the BPS monopole and dyon solutions are …
We describe a simple method for determining the strong-coupling BPS spectrum of four dimensional N=2 supersymmetric Yang-Mills theory. The idea is to represent the magnetic monopoles and dyons in terms of D-brane boundary states of a non-compact d=2 N=2 Landau-Ginzburg model. In this way the quantum truncated BPS spectrum at the origin of the moduli space can be directly mapped to the finite number of primary fields of the superconformal minimal models.
Mikhailov has constructed an infinite family of 1/8 BPS D3-branes in AdS(5) x S**5. We regulate Mikhailov's solution space by focussing on finite dimensional submanifolds. Our submanifolds are topologically complex projective spaces with symplectic form cohomologically equal to 2 pi N times the Fubini-Study Kahler class. Upon quantization and removing the regulator we find the Hilbert Space of N noninteracting Bose particles in a 3d Harmonic oscillator, a result previously conjectured by Beasley. This Hilbert Space is isomorphic to the classical chiral ring of 1/8 BPS states in N=4 Yang-Mills …
We study deformed supersymmetries in N=2 super Yang-Mills theory in the Omega-backgrounds characterized by two complex parameters $ε_1, ε_2$. When one of the $ε$-parameters vanishes, the theory has extended supersymmetries. We compute the central charge of the algebra and obtain the deformed BPS monopole equation. We examine supersymmetries preserved by the equation.
We study the BPS spectrum of the theory on a D3-brane probe in F theory. The BPS states are realized by multi-string configurations in spacetime. Only certain configurations obeying a selection rule give rise to BPS states in the four-dimensional probe theory. Using these string configurations, we determine the spectrum of N=2 SU(2) Yang-Mills. We also explore the relation between multi-string configurations, M theory membranes and self-dual strings.
We study the BPS condition in the $Ω$-deformed $\mathcal{N}=2$ super Yang-Mills theory when one of the $ε$-parameters of the background is zero. We obtain the deformed BPS equation for dyons and the formula for their central charge. In particular, we find that the deformed BPS monopole equation has axially-symmetric solution and is equivalent to the Ernst equation. The monopole charge is shown to be undeformed. We construct one-monopole solution explicitly and examine its profile.
