We obtain full moduli parameters for generic non-planar BPS networks of domain walls in an extended Abelian-Higgs model with $N$ complex scalar fields, and exhaust all exact solutions in the corresponding $\mathbb{C}P^{N -1}$ model. We develop a convenient description by grid diagrams which are polytopes determined by mass parameters of the model. To illustrate the validity of our method, we work out non-planar domain wall networks for lower $N$ in $3+1$ dimensions. In general, the networks can have compact vacuum bubbles, which are finite vacuum regions surrounded by domain walls, when the polytopes of the grid diagrams have inner vertices, and the size of bubbles can be controlled by moduli parameters. We also construct domain wall networks with bubbles in the shapes of the Platonic, Archimedean, Catalan, and Kepler-Poinsot solids.
We construct exact solutions of BPS pion domain walls in the four-dimensional $\mathcal{N}=1$ supersymmetric SU(N) chiral Lagrangian with pion masses introduced via linear and quadratic superpotentials. The model admits N discrete vacua in the center of SU(N) for the linear superpotential. In addition to the latter, new vacua appear for the quadratic superpotential. We find that the domain wall solutions of pions (Nambu-Goldstone bosons) that interpolate between a pair of (pion) vacua preserve half of supersymmetry. Contrary to our expectations, we have not been able to find domain walls invol…
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.
We have considered the multi-scalar and multi-tachyon fields living on a 3d domain wall embedded in a 5d dimensional Minkowski spacetime. The effective action for such a domain wall can be found by integrating out the normal modes as vibrating modes around the domain wall solution of a truncated 5d supergravity action. The multi-scalar tachyon potential are good enough to modeling assisted inflation scenario with multi-tachyon fields. The tachyon condensation are also briefly addressed.
We show that the BPS spectrum of pure SU(3) four-dimensional super Yang-Mills with N=2 supersymmetry exhibits a surprising phenomenon: there are regions of the Coulomb branch where the growth of the BPS degeneracies with the charge is exponential. We show this using spectral networks and independently using wall-crossing formulae and quiver methods. The computations using spectral networks provide a very nontrivial example of how these networks determine the four-dimensional BPS spectrum. We comment on some physical implications of the wild spectrum: for example, exponentially many field-theor…
We present analytical solutions of BPS domain walls in the Einstein-Maxwell flux landscape. We also remove the smeared-branes approximation and write down solutions with localized branes. In these solutions the domain walls induce strong (if not infinite) warping.
We determine the generating functions of 1/4 BPS dyons in a class of 4d $\mathcal{N}=4$ string vacua arising as CHL orbifolds of $K3 \times T^2$, a classification of which has been recently completed. We show that all such generating functions obey some simple physical consistency conditions that are very often sufficient to fix them uniquely. The main constraint we impose is the absence of unphysical walls of marginal stability: discontinuities of 1/4 BPS degeneracies can only occur when 1/4 BPS dyons decay into pairs of 1/2 BPS states. Formally, these generating functions in spacetime can be…
We explore the properties of non-BPS multi-centre extremal black holes in ungauged N=2 supergravity coupled to n_v vector multiplets, as described by solutions to the composite non-BPS linear system. After setting up an explicit description that allows for arbitrary non-BPS charges to be realised at each centre, we study the structure of the resulting solutions. Using these results, we prove that the binding energy of the composite is always positive and we show explicitly the existence of walls of marginal stability for generic choices of charges. The two-centre solutions only exist on a hype…
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 formulate supersymmetric low energy dynamics for BPS dyons in strongly-coupled N=2 Seiberg-Witten theories, and derive wall-crossing formulae thereof. For BPS states made up of a heavy core state and n probe (halo) dyons around it, we derive a reliable supersymmetric moduli dynamics with 3n bosonic coordinates and 4n fermionic superpartners. Attractive interactions are captured via a set of supersymmetric potential terms, whose detail depends only on the charges and the special Kaehler data of the underlying N=2 theories. The small parameters that control the approximation are not electric …
Consider the degeneracies of BPS bound states of one D6 brane wrapping Calabi-Yau X with D0 branes and D2 branes. When we include D4-branes wrapping Lagrangian cycle L in addition, D2-branes can end on them. These give rise to new bound states in the d=2, N=(2,2) theory of the D4 branes. We call these "open" BPS states, in contrast to closed BPS states that arise from D-branes without boundaries. Lifting this to M-theory, we show that the generating function is captured by free Fock space spanned by M2-brane particles ending on M5 branes wrapping L. This implies that the open BPS bound states …
We consider wall-crossing phenomena associated to the counting of D2-branes attached to D4-branes wrapping lagrangian cycles in Calabi-Yau manifolds, both from M-theory and matrix model perspective. Firstly, from M-theory viewpoint, we review that open BPS generating functions in various chambers are given by a restriction of the modulus square of the open topological string partition functions. Secondly, we show that these BPS generating functions can be identified with integrands of matrix models, which naturally arise in the free fermion formulation of corresponding crystal models. A parame…
In this paper quantum effects are investigated in a very special two-scalar field model having a moduli space of BPS topological defects. In a $(1+1)$-dimensional space-time the defects are classically degenerate in mass kinks, but in $(3+1)$ dimensions the kinks become BPS domain walls, all of them sharing the same surface tension at the classical level. The heat kernel/zeta function regularization method will be used to control the divergences induced by the quantum kink and domain wall fluctuations. A generalization of the Gilkey-DeWitt-Avramidi heat kernel expansion will be developed in or…
By embedding N=2 gauge theories in string theory and utilizing string dualities we map the counting of BPS states with arbitrary electric and magnetic charges to computations of an A-model topological string on an associated geometry constructed from the data of the SW curve. We show how the conjecture of Kontsevich and Soibelman regarding wall crossing, as well as a more refined version which captures the spin content of BPS states, is a natural consequence. Chern-Simons theory realized on A-branes and a twistorial construction play key roles.
We embed a new three-form vector multiplet in ${\cal N}=1$ supergravity and we show that it can be used to generate dynamically the Hilbert--Einstein term. We then recast the theory into the standard Freedman model and we argue that a pure Fayet--Iliopoulos term is in tension with the weak gravity conjecture. Finally, we couple the three-form to a super-membrane and study BPS domain walls within matter-coupled supergravity. In these models, the Planck mass takes different values on the domain wall sides.
Compactifications with D-brane and orientifold sources lead to standard gauged supergravity theories if the sources are smeared over the internal directions. It is therefore of interest to find how the solutions described by the gauged supergravity are altered by properly localising the sources. In this paper we analyse this for BPS domain wall solutions in the seven-dimensional gauged supergravity obtained from an O6 toroidal orientifold compactification in massive IIA supergravity. This is one of the simplest no-scale supergravities that can be constructed and analysed in full detail. We fin…
We study the BPS invariants for local del Pezzo surfaces, which can be obtained as the signed Euler characteristic of the moduli spaces of stable one-dimensional sheaves on the surface $S$. We calculate the Poincare polynomials of the moduli spaces for the curve classes $β$ having arithmetic genus at most 2. We formulate a conjecture that these Poincare polynomials are divisible by the Poincare polynomials of $((-K_S).β-1)$-dimensional projective space. This conjecture motivates upcoming work on log BPS numbers.
