BPS Configurations Research Articles

A note on Wilson–ʼt Hooft operators

We find explicitly the geometry of certain moduli spaces of BPS configurations in the presence of ʼt Hooft operators. This is required to compute the Operator Product Expansion of Wilson–ʼt Hooft operators in N = 4 super-Yang–Mills theory with gauge group G = PSU ( 3 ) . We verify our results by reproducing the OPE of ʼt Hooft operators predicted by S-duality.

ON REAL INTRINSIC WALL CROSSINGS

We study moduli space stabilization of a class of BPS configurations from the perspective of the real intrinsic Riemannian geometry. Our analysis exhibits a set of implications towards the stability of the D-term potentials, defined for a set of Abelian scalar fields. In particular, we show that the nature of marginal and threshold walls of stabilities may be investigated by real geometric methods. Interestingly, we find that the leading order contributions may easily be accomplished by translations of the Fayet parameter. Specifically, we notice that the various possible linear, planar, hyperplanar and the entire moduli space stability may easily be reduced to certain polynomials in the Fayet parameter. For a set of finitely many real scalar fields, it may be further inferred that the intrinsic scalar curvature defines the global nature and range of vacuum correlations. Whereas, the underlying moduli space configuration corresponds to a noninteracting basis at the zeros of the scalar curvature, where the scalar fields become uncorrelated. The divergences of the scalar curvature provide possible phase structures, viz., wall of stability, phase transition, if any, in the chosen moduli configuration. The present analysis opens up a new avenue towards the stabilization of gauge and string moduli.

Some BPS configurations of the BLG theory

We obtain BPS configurations of the BLG theory and its variant including mass terms for scalars and fermions in addition to a background field with different world-volume and R-symmetries. Three cases are considered, with world-volume symmetries SO(1,1) and SO(2) and preserving different amounts of supersymmetry. In the former case we obtain a singular configuration preserving N=(3,3) supersymmetry and an one-quarter BPS configuration corresponding to intersecting M2-M5-M5-branes. In the latter instance the BPS equations are reduced to those in the self-dual Chern–Simons theory with two complex scalars. In want of an exact solution, we find a topological vortex solution numerically in this case. Other solutions are given by combinations of domain walls.

Generalized quark-antiquark potential at weak and strong coupling

We study a two-parameter family of Wilson loop operators in N=4 supersymmetric Yang-Mills theory which interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines. These observables capture a natural generalization of the quark-antiquark potential. We calculate these loops on the gauge theory side to second order in perturbation theory and in a semiclassical expansion in string theory to one-loop order. The resulting determinants are given in integral form and can be evaluated numerically for general values of the parameters or analytically in a systematic expansion around the 1/2 BPS configuration. We comment about the feasibility of deriving all-loop results for these Wilson loops.

Semiclassical analysis of M2-brane in AdS4×S7/Z k

We start from the classical action describing a single M2-brane on AdS_4 x S^7/ Z_k and consider semiclassical fluctuaitions around a static, 1/2 BPS configuration whose shape is AdS_2 x S^1. The internal manifold S^7/ Z_k is described as a U(1) fibration over CP^3 and the static configuration is wrapped on the U(1) fiber. Then the configuration is reduced to an AdS_2 world-sheet of type IIA string on AdS_4 x CP^3 through the Kaluza-Klein reduction on the S^1. It is shown that the fluctuations form an infinite set of N=1 supermultiplets on AdS_2, for k=1,2. The set is invariant under SO(8) which may be consistent with N=8 supersymmetry on AdS_2. We discuss the behavior of the fluctuations around the boundary of AdS_2 and its relation to deformations of Wilson loop operator.

Moduli and BPS configurations of the BLG theory

We study the moduli space of scalars in the BLG theory with and without a constant background four-form field. The classical vacuum moduli space is sixteen-dimensional in the absence of the four-form field. In its presence, however, the moduli space of BPS configurations may be reduced in dimension. We exemplify this with a BPS configuration having SO(1,2) world-volume symmetry and SO(4)×SO(4) R-symmetry in the presence of a four-form field, by constructing an explicit solution.

Classification of BPS objects in $ \mathcal{N} = 6 $ Chern-Simons matter theory

We investigate BPS conditions preserving n/12 (n = 1,...,6) supersymmetries in the Aharony-Bergman-Jafferis-Maldacena (ABJM) model. The BPS equations are classified in terms of the number of preserved supercharges and remaining subgroups of the SU(4)_R symmetry. We study structures of a map between projection conditions for the supercharges in eleven dimensions and those in the ABJM model. The BPS configurations in the ABJM model can be interpreted as known BPS objects in eleven-dimensional Mtheory,such as intersecting M2, M5-branes, M-waves, KK-monopoles and M9-branes. We also show that these BPS conditions reduce to those in N = 8 super Yang-Mills theory via the standard D2-reduction procedure in a consistent way with the M-theory interpretation of the BPS conditions.

D2-brane in the Penrose limits ofAdS4×CP3

We consider a D2-brane in the pp-wave backgrounds obtained from AdS$_4\times$CP$^3$ when electric and magnetic fields have been turned on. Upon fixing the light-cone gauge, light-cone Hamiltonian and BPS configurations are obtained. In particular we study BPS configurations with electric dipole on the two sphere giant and a giant graviton rotating in transverse directions. Moreover we show that the gauge field living on the D2-brane is replaced by a scalar field in the light-cone Hamiltonian. We also present a matrix model by regularizing (quantizing) 2-brane theory.

The BPS spectrum of monopole operators in ABJM: towards a field theory description of the giant torus.

We study the BPS spectrum of monopole operators in ABJM theory. First we work out the complete spectrum of the chiral ring by using a semiclassical analysis of the field theory compactified on a two sphere. By properly taking into account the full quantization condition of monopole charges, we show that the moduli space of ABJM U(N) × U(N) theory with Chern-Simons level k,−k is a particular \( {\mathbb{Z}_k} \) cover of the symmetric product of \( Sy{m^N}\left( {{{{{\mathbb{C}^4}}} \left/ {{{\mathbb{Z}_k}}} \right.}} \right) \). This modification applies to just one brane and the other N − 1 branes see the usual \( {{{{\mathbb{C}^4}}} \left/ {{{\mathbb{Z}_k}}} \right.} \) geometry, which implies the dual gravity is still \( Ad{S^4} \times {{{{S^7}}} \left/ {{{\mathbb{Z}_k}}} \right.} \). As a byproduct of our analysis we show that the dibaryon operators are gauge invariant and dual to D4 brane giants. We also work out in detail the spectrum of fluctuations around half-BPS monopole configurations and we find candidate states for a dual BPS configuration to the giant torus solution found by Nishioka and Takayanagi in the supergravity limit. We also discuss more general BPS states.

Noncommutative baby Skyrmions

We subject the baby Skyrme model to a Moyal deformation, for unitary or Grassmannian target spaces and without a potential term. In the Abelian case, the radial BPS configurations of the ordinary noncommutative sigma model also solve the baby Skyrme equation of motion. This gives a class of exact analytic noncommutative baby Skyrmions, which have a singular commutative limit but are stable against scaling due to the noncommutativity. We compute their energies, investigate their stability and determine the asymptotic two-Skyrmion interaction.

Multi-BPS D-Vortices

We investigate the BPS configuration of the multi D-vortices produced from the D2${\bar {\rm D}}$2 system. Based on the DBI-type action with a Gaussian-type runaway potential for a complex tachyon field, the BPS limit is achieved when the tachyon profile is thin. The solution states randomly-distributed $n$ static D-vortices with zero interaction. With the obtained BPS configuration, we derive the relativistic Lagrangian which describes the dynamics of free massive D-vortices. We also discuss the 90${}^{\circ}$ and 180${}^{\circ}$ scattering of two identical D-vortices, and present its implications on the reconnection in the dynamics of cosmic superstrings.

3dCFT and multi M2-brane theory onR×S2

The radial quantization of = 8 theory in three dimensions is considered i.e. we study the = 8 BLG theory on R × S2. We present the explicit from of the Lagrangian and the corresponding supersymmetry transformations and supersymmetry algebra. We study spectrum of this theory and some of its BPS configurations.

BPS D0-D6 branes in supergravity

We analyse 1/2 BPS IIA Dp-brane supergravity solutions with B-fields and their Killing spinor equations. Via probe analysis, we rederive the supersymmetry conditions for D0-Dp with B-fields. In the case of D6 with B-fields, the D0-probe sees a multi-centred BPS configuration where the B-fields give the location of a wall of marginal stability. Finally we go beyond the probe approximation and construct a 1/8 BPS supergravity solution for a fully back-reacted D0-D6 with B-fields.

Note on generalized Janus configurations

We study several aspects of generalized Janus configuration, which includes a theta term. We investigate the vacuum structure of the theory and find that unlike the Janus configuration without theta term there is no nontrivial vacuum. We also discuss BPS soliton configuration both by supersymmetry analysis and from energy functional. The half BPS configurations could be realized by introducing transverse (p,q)-strings in original brane configuration corresponding to generalized Janus configuration. It turns out the BPS soliton could be taken as modified dyon. We discuss the solution of half BPS equations for the sharp interface case. Moreover we construct less supersymmetric Janus configuration with theta term.

A new three-algebra representation for the Superconformal Chern-Simons Theory

Based on the realization of three-algebras in terms of algebra of matrices and four-brackets [arXiv:0807.1570] we present the notion of u(N)-based extended three-algebras, which for N = 2 reproduces the Bagger-Lambert three-algebra. Using these extended three-algebras we construct an su(N) × su(N) Chern-Simons action with explicit SO(8) invariance. The dynamical fields of this theory are eight complex valued bosonic and fermionic fields in the bi-fundamental representation of the su(N) × su(N). For generic N the fermionic transformations, however, close only on a subclass of the states of this theory onto the 3d, = 6 superalgebra. In this sector we deal with four complex valued scalars and fermions, our theory is closely related to the ABJM model [arXiv:0806.1218], and hence it can be viewed as the (low energy effective) theory of N M2-branes. We discuss that our three-algebra structure suggests a picture of open M2-brane stretched between any two pairs of M2-branes. We also analyze the BPS configurations of our model.

Classification of the BPS states in Bagger-Lambert theory

We classify, in a group theoretical manner, the BPS configurations in the multiple M2-brane theory recently proposed by Bagger and Lambert. We present three types of BPS equations preserving various fractions of supersymmetries: in the first type we have constant fields and the interactions are purely algebraic in nature; in the second type the equations are invariant under spatial rotation SO(2), and the fields can be time-dependent; in the third class the equations are invariant under boost SO(1,1) and provide the eleven-dimensional generalizations of the Nahm equations. The BPS equations for different number of supersymmetries exhibit the division algebra structures: octonion, quarternion or complex.

New BPS configurations of BMN matrix theory

We explore the 1/2 BPS configurations in BMN matrix theory with SO(3) angular momentum of $SO(3)\times SO(6)$ symmetry. The fluctuation analysis of the BPS configurations near the abelian solutions and also the fuzzy two sphere vacua reveals how nonabelian BPS configurations emerge. Especially the irreducible nonabelian configurations seem to have the maximal angular momentum of order $N^3$, beyond which they collapse to abelian ones. We also find some new BPS configurations explicitly.

Matrix model maps and reconstruction of AdS supergravity interactions

We consider the question of reconstructing (cubic) SUGRA interactions in AdS/CFT. The method we introduce is based on the matrix model maps (MMP) which were previously successfully employed at the linearized level. The strategy is to start with the map for $1/2$ BPS configurations, which is exactly known (to all orders) in the Hamiltonian framework. We then use the extension of the matrix model map with the corresponding Ward identities to completely specify the interaction. A central point in this construction is the nonvanishing of off-shell interactions (even for highest-weight states).

Noncommutative D-branes from covariant AdS superstring

We study noncommutative (NC) D-branes on AdS 5 × S 5 from κ-invariance of covariant Green–Schwarz action of an open string with a non-trivial world-volume flux. Finding boundary conditions to ensure the κ-invariance, we can see possible configurations of the NC D-branes. With this method 1/4 BPS NC D-branes are discussed. The resulting NC D p-branes are 1/4 BPS at arbitrary position other than the p = 1 case. The exceptional D-string is 1/2 BPS at the origin and 1/4 BPS outside the origin. Those are reduced to possible 1/4 BPS or 1/2 BPS AdS D-branes in the commutative limit. The same analysis is applied to an open superstring in a pp-wave and leads to 1/4 BPS configurations of NC D-branes. These D-branes are consistently obtained from AdS D-branes via the Penrose limit.

All 1/2 BPS solutions of IIB supergravity with [formula omitted] isometry

In hep-th/0409174, Lin, Lunin and Maldacena constructed a set of regular 1/2 BPS geometries in IIB theory. These remarkable ‘bubbling AdS’ geometries have a natural interpretation as duals of chiral primary operators with weight Δ=J in N=4 super-Yang–Mills theory. Although these geometries have been assumed to be complete, from a purely supergravity point of view, additional 1/2 BPS configurations may potentially exist with a preferred null isometry. We explore this possibility and prove that the only additional class of 1/2 BPS solutions with SO(4)×SO(4) isometry are the familiar IIB pp-waves.