non-BPS States Research Articles

Galois groups of uplifted de Sitter vacua

We compute the Galois group of a polynomial whose roots are determined by the critical points of a scalar potential in type IIB compactifications. We focus our study on certain perturbative models where it is feasible to construct a de Sitter vacuum within the effective theory by introducing non-geometric fluxes, D-branes or non-BPS states. Our findings clearly show that all de Sitter vacua derived from lifting AdS stable vacua are associated with an unsolvable Galois group. This suggests a deeper connection between the fundamental principles of Galois theory and its applications in the construction of dS vacua.

The asymptotic weak gravity conjecture in M-theory

The tower Weak Gravity Conjecture predicts infinitely many super-extremal states along every ray in the charge lattice of a consistent quantum gravity theory. We show this far-reaching claim in five-dimensional compactifications of M-theory on Calabi-Yau 3-folds for gauge groups with a weak coupling limit. We first characterize the possible weak coupling limits, building on an earlier classification of infinite distance limits in the Kähler moduli space of M-theory compactifications. We find that weakly coupled gauge groups are associated to curves on the compactification space contained in generic fibers or in fibers degenerating at finite distance in their moduli space. These always admit an interpretation as a Kaluza-Klein or winding U(1) in a dual frame or as part of a dual perturbative heterotic gauge group, in agreement with the Emergent String Conjecture. Using the connection between Donaldson-Thomas invariants and Noether-Lefschetz theory, we then show that every ray in the associated charge lattice either supports a tower of BPS states or of non-BPS states, and prove that these satisfy the super-extremality condition, at least in the weak coupling regime.

Some remarks on Swampland conjectures, fluxes and K-theory in IIB toroidal compactifications

In this note, we present a scenario in which the existence of dS vacua is jeopardized by topological transitions between non-BPS branes and fluxes in type IIB toroidal compactifications. We focus our study on a six-dimensional torus compactification modded out by an orientifold three-plane. In particular, we consider the presence of non-BPS five branes, which allows the construction of apparent stable dS vacua. Since moduli stabilization requires the presence of NS–NS fluxes, we also describe the minimal required conditions to avoid the appearance of Freed–Witten anomalies. Cancellation of these anomalies implies a topological transformation between non-BPS states and fluxes with the same discrete K-theory charge. After the transition, we observe that the scalar potential undergoes major changes, implying that the dS vacua are unstable. We discuss a scenario in which, even if the discrete K-theory charge is globally canceled, the above transitions could still be relevant, allowing the existence of short-lived dS minima. We briefly comment on how these implications seem to be in concordance with the Refined de Sitter and Trans-Planckian Censorship Conjectures.

Metastable vacua from torsion and machine learning

By implementing an error function on a Machine Learning algorithm we look for minimal conditions to construct stable Anti de Sitter and de Sitter vacua from dimensional type IIB String theory compactification on Kähler manifolds with torsion. This allows to have contributions to the scalar potential from the five-form flux and from D-branes wrapping torsional cycles, interpreted as non-BPS states. The former implies the possibility to construct stable AdS vacua while the latter constitutes a mechanism to uplift AdS to dS vacua. Particularly we consider {widehat{D5}} non-BPS states to uplift the stable AdS vacua to an (apparently) stable dS minimum. Both results – the generation of an AdS vacuum and the corresponding uplifting to a dS one – are restricted to a certain type of configurations, specifically with the number of O3 orientifolds bounded from below by the number of D3-branes and fluxes. Under these conditions, we report over 170 dS (classical) stable vacua. In all of them, the uplifted effective potential becomes very flat indicating the presence of possible sources of instabilities. We comment on their relationship with the Swampland Conjectures.

Non-BPS supersymmetric 3pt amplitude for one massless, two equally massive particles

In this paper, the non-BPS amplitudes (Z<2m) are considered. Utilizing on-shell methods, the three point amplitudes of two equal-mass particles and one massless particle were constructed, where the two massive particles are non-BPS states. We verify the result by matching the Z=0 and BPS limit with N=2 supersymmetry. As an application we derive the non-BPS coupling for N=4 super-Maxwell and supergravity.

Half-BPS vertex operators of the AdS5 \xd7 S5 superstring

Using the pure spinor formalism for the superstring in an AdS5 × S5 background, a simple expression is found for half-BPS vertex operators. At large radius, these vertex operators reduce to the usual supergravity vertex operators in a flat background. And at small radius, there is a natural conjecture for generalizing these vertex operators to non-BPS states.

Topological solitons in the supersymmetric Skyrme model

A supersymmetric extension of the Skyrme model was obtained recently, which consists of only the Skyrme term in the Nambu-Goldstone (pion) sector complemented by the same number of quasi-Nambu-Goldstone bosons. Scherk-Schwarz dimensional reduction yields a kinetic term in three or lower dimensions and a potential term in two dimensions, preserving supersymmetry. Euclidean solitons (instantons) are constructed in the supersymmetric Skyrme model. In four dimensions, the soliton is an instanton first found by Speight. Scherk-Schwarz dimensional reduction is then performed once to get a 3-dimensional theory in which a 3d Skyrmion-instanton is found and then once more to get a 2d theory in which a 2d vortex-instanton is obtained. Although the last one is a global vortex it has finite action in contrast to conventional theory. All of them are non-BPS states breaking all supersymmetries.

A ladder of topologically non-trivial non-BPS states

We consider a simple quiver gauge theory with gauge group U ( r 1 ) × U ( r 2 ) and a Higgs field in the bi-fundamental representation. The background for this theory is a compact Kähler manifold M . For a careful but natural choice of Higgs field potential the second order field equations can be replaced with a set of first order BPS equations. We show that the theory admits two energy gaps: The vacuum is topologically trivial but has finite, non-zero energy and is not a BPS state. The second gap lies between the vacuum and the first BPS state. In this gap we find a ladder of states with non-trivial topology, at equidistant energy levels. We give a semi-explicit construction for such topologically non-trivial non-BPS states.

S-duality improved perturbation theory in compactified type I/heterotic string theory

We study the mass of the stable non-BPS state in type I / heterotic string theory compactified on a circle with the help of the interpolation formula between weak and strong coupling results. Comparison between the results at different orders indicate that this procedure can determine the mass of the particle to within 10% accuracy over the entire two dimensional moduli space parametrized by the string coupling and the radius of compactification. This allows us to estimate the region of the stability of the particle in this two dimensional moduli space. Outside this region the particle is unstable against decay into three BPS states carrying the same total charge as the original state. We discuss generalization of this analysis to compactification on higher dimensional tori.

Three-point functions in the SU(2) sector at strong coupling

Extending the methods developed in our previous works (arXiv:1110.3949, arXiv:1205.6060), we compute the three-point functions at strong coupling of the non-BPS states with large quantum numbers corresponding to the composite operators belonging to the so-called SU(2) sector in the $\mathcal{N}=4$ super-Yang-Mills theory in four dimensions. This is achieved by the semi-classical evaluation of the three-point functions in the dual string theory in the $AdS_3 \times S^3$ spacetime, using the general one-cut finite gap solutions as the external states. In spite of the complexity of the contributions from various parts in the intermediate stages, the final answer for the three-point function takes a remarkably simple form, exhibiting the structure reminiscent of the one obtained at weak coupling. In particular, in the Frolov-Tseytlin limit the result is expressed in terms of markedly similar integrals, however with different contours of integration. We discuss a natural mechanism for introducing additional singularities on the worldsheet without affecting the infinite number of conserved charges, which can modify the contours of integration.

S-duality improved superstring perturbation theory

Strong - weak coupling duality in string theory allows us to compute physical quantities both at the weak coupling end and at the strong coupling end. Furthermore perturbative string theory can be used to compute corrections to the leading order formula at both ends. We explore the possibility of constructing a smooth interpolating formula that agrees with the perturbation expansion at both ends and leads to a fairly accurate determination of the quantity in consideration over the entire range of the coupling constant. We apply this to study the mass of the stable non-BPS state in SO(32) heterotic / type I string theory with encouraging results. In particular our result suggests that after taking into account one loop corrections to the mass in the heterotic and type I string theory, the interpolating function determines the mass within 10% accuracy over the entire range of coupling constant.

Counting charged massless states in the (0, 2) heterotic CFT/geometry connection

We use simple current techniques and their relation to orbifolds with discrete torsion for studying the (0, 2) CFT/ geometry duality with non-rational internal $ \mathcal{N} = 2 $ SCFTs. Explicit formulas for the charged spectra of heterotic SO(10) GUT models are computed in terms of their extended Poincaré polynomials and the complementary Poincaré polynomial which can be computed in terms of the elliptic genera. While non-BPS states contribute to the charged spectrum, their contributions can be determined also for non-rational cases. For model building, with generalizations to SU(5) and SM gauge groups, one can take advantage of the large class of Landau-Ginzburg orbifold examples.

KO-HOMOLOGY AND TYPE I STRING THEORY

We study the classification of D-branes and Ramond–Ramond fields in Type I string theory by developing a geometric description of KO-homology. We define an analytic version of KO-homology using KK-theory of real C*-algebras, and construct explicitly the isomorphism between geometric and analytic KO-homology. The construction involves recasting the C ℓn-index theorem and a certain geometric invariant into a homological framework which is used, along with a definition of the real Chern character in KO-homology, to derive cohomological index formulas. We show that this invariant also naturally assigns torsion charges to non-BPS states in Type I string theory, in the construction of classes of D-branes in terms of topological KO-cycles. The formalism naturally captures the coupling of Ramond–Ramond fields to background D-branes which cancel global anomalies in the string theory path integral. We show that this is related to a physical interpretation of bivariant KK-theory in terms of decay processes on spacetime-filling branes. We also provide a construction of the holonomies of Ramond–Ramond fields in Type II string theory in terms of topological K-chains.

BPS and non-BPS kinks in a massive nonlinearS2-sigma model

The stability of the topological kinks of the nonlinear S{sup 2}-sigma model discovered by Alonso Izquierdo et al. is discussed by means of a direct estimation of the spectra of the second-order fluctuation operators around topological kinks. The one-loop mass shifts caused by quantum fluctuations around these kinks are computed using the Cahill-Comtet-Glauber formula. The (lack of) stability of the nontopological kinks is unveiled by application of the Morse index theorem. These kinks are identified as non-BPS states. There are two types of topological kinks coming from the twofold embedding of the sine-Gordon model in the massive nonlinear sigma model. It is shown that sine-Gordon kinks of only one type satisfy first-order equations and are accordingly BPS classical solutions. Finally, the interplay between instability and supersymmetry is explored.

Dyon dynamics near marginal stability and non-BPS states

We derive the general form of the moduli-space effective action for the long-range interaction of two BPS dyons in N=2 gauge theories. This action determines the bound state structure of various BPS and non-BPS states near marginal stability curves, and we utilise it to compute the leading correction to the BPS-mass of zero-torsion non-BPS bound states close to marginal stability.

STABILITY EQUATION AND TWO-COMPONENT EIGENMODE FOR DOMAIN WALLS IN A SCALAR POTENTIAL MODEL

The connection between the supersymmetric quantum mechanics involving two-component eigenfunctions and the stability equation associated with two classical configurations is investigated and a matrix superpotential is deduced. The question of stability is ensured for the Bogomol'nyi–Prasad–Sommerfield (BPS) states on two domain walls in a scalar potential model containing up to fourth-order powers in the fields, which is explicit demonstrated using the intertwining operators in terms of two-by-two matrix superpotential in the algebraic framework of supersymmetry in quantum mechanics. Also, a non-BPS state is found to be nonstable via the fluctuation Hessian matrix.

Decoding the matrix: Coincident membranes on the plane wave

At the core of nonperturbative theories of quantum gravity lies the holographic encoding of bulk data in large matrices. At present this mapping is poorly understood. The plane wave matrix model provides a laboratory for isolating aspects of this problem in a controlled setting. At large boosts, configurations of concentric membranes become superselection sectors, whose exact spectra are known. From the bulk point of view, one expects product states of individual membranes to be contained within the full spectrum. However, for non-BPS states this inclusion relation is obscured by Gauss law constraints. Its validity rests on nontrivial relations in representation theory, which we identify and verify by explicit computation.

Non-perturbative orientifold transitions at the conifold

After orientifold projection, the conifold singularity in hypermultiplet moduli space of Calabi-Yau compactifications cannot be avoided by geometric deformations. We study the non-perturbative fate of this singularity in a local model involving O6-planes and D6-branes wrapping the deformed conifold in Type IIA string theory. We classify possible A-type orientifolds of the deformed conifold and find that they cannot all be continued to the small resolution. When passing through the singularity on the deformed side, the O-plane charge generally jumps by the class of the vanishing cycle. To decide which classical configurations are dynamically connected, we construct the quantum moduli space by lifting the orientifold to M-theory as well as by looking at the superpotential. We find a rich pattern of smooth and phase transitions depending on the total sixbrane charge. Non-BPS states from branes wrapped on non-supersymmetric bolts are responsible for a phase transition. We also clarify the nature of a Z_2 valued D0-brane charge in the 6-brane background. Along the way, we obtain a new metric of G_2 holonomy corresponding to an O6-plane on the three sphere of the deformed conifold.

Multi-spin string solutions in AdS5× S5

Motivated by attempts to extend AdS/CFT duality to non-BPS states we consider classical closed string solutions with several angular momenta in different directions of AdS 5 and S 5. We find a novel solution describing a circular closed string located at a fixed value of AdS 5 radius while rotating simultaneously in two planes in AdS 5 with equal spins S. This solution is a direct generalization of a two-spin flat-space solution where the string rotates in two orthogonal planes while always lying on a 3-sphere. Similar solution exists for a string rotating in S 5: it is parametrized by the angular momentum J of the center of mass and two equal SO(6) angular momenta J 2= J 3= J′ in the two rotation planes. The remarkably simple case is of J=0 where the energy depends on J′ as E= (2J′) 2+λ ( λ is the string tension or 't Hooft coupling). We discuss interpolation of the E( J′) formula to weak coupling by identifying the gauge theory operator that should be dual to the corresponding semiclassical string state and utilizing existing results for its perturbative anomalous dimension. This opens up a possibility of studying AdS/CFT duality in this new non-BPS sector. We also investigate small fluctuations and stability of these classical solutions and comment on several generalizations.

BPS and non-BPS states in a supersymmetric Landau-Ginzburg theory

We analyze the spectrum of the N=(2,2) supersymmetric Landau-Ginzburg theory in two dimensions with superpotential W=X^{n+2}-lambda X^2. We find the full BPS spectrum of this theory by exploiting the direct connection between the UV and IR limits of the theory. The computation utilizes results from the Picard-Lefschetz theory of singularities and its extension to boundary singularities. The additional fact that this theory is integrable requires that the BPS states do not close under scattering. This observation fixes the masses of non-BPS states as well.