BPS String Research Articles

On SYM theory and all order bulk singularity structures of BPS strings in type II theory

The complete forms of the S-matrix elements of a transverse scalar field, two world volume gauge fields, and a Potential Cn−1 Ramond–Ramond (RR) form field are investigated. In order to find an infinite number of t,s,(t+s+u)-channel bulk singularity structures of this particular mixed open-closed amplitude, we employ all the conformal field theory techniques to <VC−2Vϕ0VA0VA0>, exploring all the entire correlation functions and all order α′ contact interactions to these supersymmetric Yang–Mills (SYM) couplings. Singularity and contact term comparisons with the other symmetric analysis, <VC−1Vϕ0VA−1VA0> and <VC−1Vϕ−1VA0VA0> are also carried out in detail. Various couplings from pull-Back of branes, Myers terms and several generalized Bianchi identities should be taken into account to be able to reconstruct all order α′ bulk singularities of type IIB (IIA) superstring theory. Finally, we make a comment on how to derive without any ambiguity all order α′ contact terms of this S-matrix which carry momentum of RR in transverse directions.

On exceptional instanton strings

According to a recent classification of 6d (1, 0) theories within F-theory there are only six “pure” 6d gauge theories which have a UV superconformal fixed point. The corresponding gauge groups are SU(3), SO(8), F4, E6, E7, and E8. These exceptional models have BPS strings which are also instantons for the corresponding gauge groups. For G simply-laced, we determine the 2d mathcal{N}=left(0,4right) worldsheet theories of such BPS instanton strings by a simple geometric engineering argument. These are given by a twisted S2 compactification of the 4d mathcal{N}=2 theories of type H2, D4, E6, E7 and E8 (and their higher rank generalizations), where the 6d instanton number is mapped to the rank of the corresponding 4d SCFT. This determines their anomaly polynomials and, via topological strings, establishes an interesting relation among the corresponding T2× S2 partition functions and the Hilbert series for moduli spaces of G instantons. Such relations allow to bootstrap the corresponding elliptic genera by modularity. As an example of such procedure, the elliptic genera for a single instanton string are determined. The same method also fixes the elliptic genus for case of one F4 instanton. These results unveil a rather surprising relation with the Schur index of the corresponding 4d mathcal{N}=2 models.

On bulk singularity structures and all order α ′ contact terms of BPS string amplitudes

The entire form of the amplitude of three SYM ( involving two transverse scalar fields, a gauge field) and a potential $C_{n-1}$ Ramond-Ramond (RR) form field is found out. We first derive $<V_{C^{-2}} V_{A^{0}} V_{\phi ^{0}} V_{\phi ^{0}}>$ and then start constructing an infinite number of $t,s$ channel bulk singularity structures by means of all order $\alpha'$ corrections to pull-back of brane in an Effective Field Theory (EFT). Due to presence of the complete form of S-matrix, several new contact interactions as well as new couplings are explored. It is also shown that these couplings can be verified at the level of EFT by either the combinations of Myers terms, pull-back, Taylor expanded of scalar fields or the mixed combination of the couplings of this paper as well as employed Bianchi identities. For the first time, we also derive the algebraic and the complete form of the integrations for some arbitrary combinations of Mandelstam variables and for the most general case $\int d^2z |1-z|^{a} |z|^{b} (z - \bar{z})^{c} (z + \bar{z})^{3}$ on upper half plane as well.

On RR couplings, singularity structures and all order α′ contact interactions to BPS string amplitudes

We evaluate five point world-sheet string theory amplitudes of one transverse scalar field, two world volume gauge fields (and two transverse scalars, a gauge field) in the presence of a closed string Ramond-Ramond vertex operator in its symmetric picture. We carry out all the entire S-matrix elements of five point mixed RR-scalars/gauge fields <C −1 ϕ 0 A −1 A 0>, <C −1 ϕ −1 A 0 A 0>, <C −1 A 0 ϕ −1 ϕ 0> and <C −1 A −1 ϕ 0 ϕ 0> in detail and start comparing all order α′ contact interactions and singularities in both transverse and world volume directions. We explore the presence of various new couplings in string theory effective actions and find out their all order α′ higher derivative corrections in both type IIA and IIB. Ultimately we make various remarks for the singularities and contact terms whose RR momenta are embedded in transverse directions. α′ corrections to some of Myers terms are also addressed.

Q-balls of quasi-particles in a (2, 0)-theory model of the fractional quantum Hall effect

A toy model of the fractional quantum Hall effect appears as part of the low-energy description of the Coulomb branch of the A 1 (2, 0)-theory formulated on $$ \left({S}^1\times {\mathrm{\mathbb{R}}}^2\right)/{\mathrm{\mathbb{Z}}}_k $$ , where the generator of $$ {\mathrm{\mathbb{Z}}}_k $$ acts as a combination of translation on S 1 and rotation by 2π/k on $$ {\mathrm{\mathbb{R}}}^2 $$ . At low energy the configuration is described in terms of a 4+1D Super-Yang-Mills theory on a cone $$ \left({\mathrm{\mathbb{R}}}^2/{\mathrm{\mathbb{Z}}}_k\right) $$ with additional 2+1D degrees of freedom at the tip of the cone that include fractionally charged particles. These fractionally charged “quasi-particles” are BPS strings of the (2, 0)-theory wrapped on short cycles. We analyze the large k limit, where a smooth cigar-geometry provides an alternative description. In this framework a W-boson can be modeled as a bound state of k quasi-particles. The W-boson becomes a Q-ball, and it can be described as a soliton solution of Bogomolnyi monopole equations on a certain auxiliary curved space. We show that axisymmetric solutions of these equations correspond to singular maps from AdS 3 to AdS 2, and we present some numerical results and an asymptotic expansion.

Semiclassical strings in marginally deformed toric AdS/CFT

We study string solutions in the beta-deformed Sasaki-Einstein gauge/gravity dualities. We find that the BPS point-like strings move in the submanifolds where the two U(1) circles shrink to zero size. In the corresponding T^3 fibration description, the strings live on the edges of the polyhedron, where the T^3 fibration degenerates to T^1. Moreover, we find that for each deformed Sasaki-Einstein manifold the BPS string solutions exist only for particular values of the deformation parameter. Our results imply that in the dual field theory the corresponding BPS operators exist only for these particular values of the deformation parameter we find. We also examine the non-BPS strings, derive their dispersion relations and compare them with the undeformed ones. Finally, we comment on the range of the validity of our solutions and their dependence on the deformation parameter.

String Solutions in Sasaki-Einstein Manifolds and their marginally deformed versions

We review some recent results on string solutions in the Sasaki-Einstein manifolds and their marginally β-deformed versions. We discuss both BPS and non-BPS string solutions, some of their properties and their energy-spin relations.

On hybrid (topologically) massive supergravity in three dimensions

A class of hybrid (topologically) massive off-shell supergravities coupled to an on-shell matter scalar multiplet was recently constructed. The auxiliary field in the off-shell multiplet is dynamical for generic values of the eight parameters. We find that by choosing the parameters appropriately, it remains non-dynamical. We perform linearized analysis around the supersymmetric AdS3 vacuum and its Minkowski limit. The ghost-free condition for the Minkowski vacuum is explored. For the AdS3 vacuum, we obtain the criticality condition and find that at the critical points, one of the two massive gravitons becomes pure gauge and decouples from the bulk physics, whilst the other has positive energy. We demonstrate that the mass of the BTZ black hole is non-negative at the critical points. We also investigate general BPS solutions. For certain parameter choices, we obtain exact solutions. In particular, we present the BPS string (domain-wall) solution that is dual to certain two-dimensional quantum field theory with an ultra-violet conformal fixed point.

Non-simply laced Lie algebras via F theory strings

In order to describe the appearance in F theory of the non--simply--laced Lie algebras, we use the representation of symmetry enhancements by means of string junctions. After an introduction to the techniques used to describe symmetry enhancement, that is algebraic geometry, BPS states analysis and string junctions, we concentrate on the latter. We give an explicit description of the folding of D_{2n} to B_n of the folding of E_6 to F_4 and that of D_4 to G_2 in terms of junctions and Jordan strings. We also discuss the case of C_n, but we are unable in this case to provide a string interpretation.

BPS open strings and A-D-E-singularities in F-theory on K3

We improve on a recently constructed graphical representation of the supergravity 7-brane solution and apply this refined representation to re-study the open string description of the A-D-E-singularities in F-theory on K3. A noteworthy feature of the graphical representation is that it provides the complete global branch cut structure of the 7-brane solution which plays an important role in our analysis. We first identify those groups of branes which when made to coincide lead to the A-D-E-gauge groups. We next show that there is always a sufficient number of open BPS strings to account for all the generators of the gauge group. However, as we will show, there is in general no one-to-one relation between BPS strings and gauge group generators.For the \( {D_{n + {4^{-} }}} \) and E-singularities, in order to relate BPS strings with gauge group generators, we make an SU(n + 4), respectively SU(5) subgroup of the \( {D_{n + {4^{-} }}} \) and E-gauge groups manifest. We find that only for the D-series (and for the standard A-series) this is sufficient to identify, in a one-to-one manner, which BPS strings correspond to which gauge group generators.

String solitons in the M5-brane worldvolume with a Nambu-Poisson structure and Seiberg-Witten map

We analyze BPS equations for string-like configurations derived from the M5-brane worldvolume action with a Nambu-Poisson structure constructed in ref. [1, 2]. We solve the BPS equations up to the first order in the parameter g which characterizes the strength of the Nambu-Poisson bracket. We compare our solutions to previously constructed BPS string solitons in the conventional description of M5-brane in a constant three-form background via Seiberg-Witten map, and find agreement.

STRING THEORY EFFECTS ON FIVE-DIMENSIONAL BLACK HOLE PHYSICS

We review recent developments in understanding quantum/string corrections to BPS black holes and strings in five-dimensional supergravity. These objects are solutions to the effective action obtained from M-theory compactified on a Calabi–Yau threefold, including the one-loop corrections determined by anomaly cancellation and supersymmetry. We introduce the off-shell formulation of this theory obtained through the conformal supergravity method and review the methods for investigating supersymmetric solutions. This leads to quantum/string corrected attractor geometries, as well as asymptotically flat black strings and spinning black holes. With these solutions in hand, we compare our results with analogous studies in four-dimensional string-corrected supergravity, emphasizing the distinctions between the four- and five-dimensional theories.

Strings and D-branes in a supersymmetric magnetic flux background

We investigate how the presence of RR magnetic Fp+2 fluxes affects the energy of classical Dp branes, for specific string theory supersymmetric backgrounds which are solutions to the leading order in α' including back-reaction effects. The Dp brane dynamics is found to be similar to the well known dynamics of particles and strings moving in magnetic fields. We find a class of BPS solutions which generalize the BPS fundamental strings or BPS branes with momentum and winding to the case of non-zero magnetic fields. Remarkably, the interaction with the magnetic fields does not spoil the supersymmetry of the solution, which turns out to be invariant under four supersymmetry transformations. We find that magnetic fields can significantly reduce the energy of some BPS strings and Dp branes, in particular, some macroscopic Dp branes become light for sufficiently large magnetic fields.

BPS string webs in the 6-dim (2,0) theories

In the Coulomb phase of the 6-dim (2,0) superconformal theories, the 1/4, 1/8, 1/16 BPS selfdual string webs are argued to exist such that the spatial SO(5) and internal SO(5) rotations are correlated. The basic constituents are 1/2 BPS strings and 1/4 BPS string junctions. One support comes from the existence of the similar BPS dyonic monostring webs in 5-dim maximally supersymmetric gauge theories. Another comes from the study of the supersymmetry of the intersecting M2 brane stripes terminating on M5 branes. We also discuss the related BPS webs in little string theories and other theories.

Loop space, (2,0) theory, and solitonic strings

We present an interacting action that lives in loop space, and we argue that this is a generalization of the theory for a free tensor multiplet. From this action we derive the Bogomolnyi equation corresponding to solitonic strings. Using the Hopf map, we find a correspondence between BPS strings and BPS monopoles in four-dimensional super Yang-Mills theory. This enable us to find explicit BPS saturated solitonic string solutions.

1/4 BPS circular loops, unstable world-sheet instantons and the matrix model

The standard prescription for computing Wilson loops in the AdS/CFT correspondence in the large coupling regime and tree-level involves minimizing the string action. In many cases the action has more than one saddle point as in the simple example studied in this paper, where there are two 1/4 BPS string solutions, one a minimum and the other not. Like in the case of the regular circular loop the perturbative expansion seems to be captured by a free matrix model. This gives enough analytic control to extrapolate from weak to strong coupling and find both saddle points in the asymptotic expansion of the matrix model. The calculation also suggests a new BMN-like limit for nearly BPS Wilson loop operators.

Non-Abelian semilocal strings inN=2supersymmetric QCD

We consider a benchmark bulk theory in four-dimensions: N=2 supersymmetric QCD with the gauge group U(N) and N_f flavors of fundamental matter hypermultiplets (quarks). The nature of the BPS strings in this benchmark theory crucially depends on N_f. If N_f\geq N and all quark masses are equal, it supports non-Abelian BPS strings which have internal (orientational) moduli. If N_f>N these strings become semilocal, developing additional moduli \rho related to (unlimited) variations of their transverse size. Using the U(2) gauge group with N_f=3,4 as an example, we derive an effective low-energy theory on the (two-dimensional) string world sheet. Our derivation is field-theoretic, direct and explicit: we first analyze the Bogomol'nyi equations for string-geometry solitons, suggest an ansatz and solve it at large \rho. Then we use this solution to obtain the world-sheet theory. In the semiclassical limit our result confirms the Hanany-Tong conjecture, which rests on brane-based arguments, that the world-sheet theory is N=2 supersymmetric U(1) gauge theory with N positively and N_e=N_f-N negatively charged matter multiplets and the Fayet-Iliopoulos term determined by the four-dimensional coupling constant. We conclude that the Higgs branch of this model is not lifted by quantum effects. As a result, such strings cannot confine. Our analysis of infrared effects, not seen in the Hanany-Tong consideration, shows that, in fact, the derivative expansion can make sense only provided the theory under consideration is regularized in the infrared, e.g. by the quark mass differences. The world-sheet action discussed in this paper becomes a bona fide low-energy effective action only if \Delta m_{AB}\neq 0.

CosmicD-strings as axionicD-term strings

In this work we derive non-singular BPS string solutions from an action that captures the essential features of a D-brane-anti-D-brane system compactified to four dimensions. The model we consider is a supersymmetric abelian Higgs model with a D-term potential coupled to an axion-dilaton multiplet. The strings in question are axionic D-term strings which we identify with the D-strings of type II string theory. In this picture the Higgs field represents the open string tachyon of the D-Dbar pair and the axion is dual to a Ramond Ramond form. The crucial term allowing the existence of non-singular BPS strings is the Fayet-Iliopoulos term, which is related to the tensions of the D-string and of the parent branes. Despite the presence of the axion, the strings are BPS and carry finite energy, due to the fact that the space gets very slowly decompactified away from the core, screening the long range axion field (or equivalently the theory approaches an infinitely weak 4D coupling). Within our 4D effective action we also identify another class of BPS string solutions (s-strings) which have no ten dimensional analog, and can only exist after compactification.

Non-Abelian flux tubes inN=1SQCD: Supersizing world-sheet supersymmetry

We consider non-Abelian 1/2 BPS flux tubes (strings) in a deformed N=2 supersymmetric gauge theory, with mass terms mu_{1,2} of the adjoint fields breaking N=2 down to N=1. The main feature of the non-Abelian strings is the occurrence of orientational moduli associated with the possibility of rotations of their color fluxes inside a global SU(N) group. The bulk four-dimensional theory has four supercharges; half-criticality of the non-Abelian strings would imply then N=1 supersymmetry on the world sheet, i.e. two supercharges. In fact, superalgebra of the reduced moduli space has four supercharges. Internal dynamics of the orientational moduli are described by two-dimensional CP(N-1) model on the string world sheet. We focus mainly on the SU(2) case, i.e. CP(1) world-sheet theory. We show that non-Abelian BPS strings exist for all values of mu_{1,2}. The low-energy theory of moduli is indeed CP(1), with four supercharges, in a wide region of breaking parameters mu_{1,2}. Only in the limit of very large mu_{1,2}, above some critical value, the N=2 world-sheet supersymmetry breaks down to N=1. We observe "supersymmetry emergence" for the flux-tube junction (confined monopole): the "kink-monopole" is half-critical considered from the standpoint of the world-sheet CP(1) model (i.e. two supercharges conserved), while in the bulk N=1 theory there is no monopole central charge at all.

Color superconductivity, BPS Zk strings and monopole confinement in N = 2 and N = 4 super Yang-Mills theories

We review some recent developments on BPS string solutions and monopole confinement in the Higgs (or color) superconducting phase of <IMG SRC="/img/revistas/bjp/v34n4a/caln_mai.gif" > or = 2 and <IMG SRC="/img/revistas/bjp/v34n4a/caln_mai.gif" > or = 4 super Yang-Mills theories. In particular, the monopole magnetic fluxes are shown to be always integer linear combinations of string fluxes. Moreover, a bound for the threshold length of the string breaking is obtained. When the gauge group SU(N) is broken to Z N, the BPS string tension satisfies the Casimir scaling law. Furthermore, in the SU(3) case the string solutions are such that they allow the formation of a confining system with three monopoles.