Brane Intersections Research Articles

Yukawa couplings at infinite distance and swampland towers in chiral theories

We study limits of vanishing Yukawa couplings of 4d chiral matter fields in Quantum Gravity, using as a laboratory type IIA orientifolds with D6-branes. In these theories chiral fermions arise at brane intersections, where an infinite tower of charged particles dubbed gonions are localised. We show that in the limit Y → 0 some of these towers become asymptotically massless, while at the same time the kinetic term of some chiral fields becomes singular and at least two extra dimensions decompactify. For limits parametrised by a large complex structure saxion u, Yukawa couplings have a behaviour of the form Y ~ 1/ur, with r some positive rational number. Moreover, in this limit some of the gauge couplings associated to the Yukawa vanish. The lightest gonion scales are of order mgon ~ gsMP with s > 1, verifying the magnetic WGC with room to spare and with no need of its tower/sublattice versions. We also show how this behaviour can be understood in the context of the emergence of kinetic terms in Quantum Gravity. All these results may be very relevant for phenomenology, given the fact that some of the Yukawa couplings in the Standard Model are very small.

Intersecting end of the world branes

Dynamical cobordisms implement the swampland cobordism conjecture in the framework of effective field theory, realizing codimension-1 end of the world (ETW) branes as singularities at finite spacetime distance at which scalars diverge to infinite field space distance. ETW brane solutions provide a useful probe of infinity in moduli/field spaces and the associated swampland constraints, such as the distance conjecture.We construct explicit solutions describing intersecting ETW branes in theories with multiple scalars and general potentials, so that different infinite field space limits coexist in the same spacetime, and can be simultaneously probed by paths approaching the ETW brane intersection. Our class of solutions includes physically interesting examples, such as intersections of Witten’s bubbles of nothing in toroidal compactifications, generalizations in compactifications on products of spheres, and possible flux dressings thereof (hence including charged objects at the ETW branes). From the cobordism perspective, the intersections can be regarded as describing the end of the world for end of the world branes, or as boundary domain walls interpolating between different ETW brane boundary conditions for the same bulk theory.

Supersymmetric solutions of type-II supergravity from λ-deformations and zoom-in limits

We construct the embedding of the λ-model on SL(2, ℝ) × SU(2) × SU(2) in type-II supergravity. In the absence of deformation, the ten-dimensional background corresponds to the near-horizon limit of the NS1-NS5-NS5 brane intersection. We show that when the deformation is turned on, supersymmetry breaks by half, and the solution preserves 8 supercharges. The Penrose limits along two null geodesics of the deformed geometry are also considered. It turns out that none of the associated plane-wave backgrounds exhibit supernumerary supercharges.

Supersymmetric backgrounds from λ-deformations

We provide the first supersymmetric embedding of an integrable λ-deformation to type-II supergravity. Specifically, that of the near horizon of the NS1-NS5 brane intersection, geometrically corresponding to AdS3 × S3 × T4. We show that the deformed background preserves 1/4 of the maximal supersymmetry. In the Penrose limit we show that it preserves no-more than one half of the maximal supersymmetry.

AdS2 near-horizons, defects, and string dualities

We construct a new family of $\text{AdS}_2\times S^3\times S^2$ solutions to Type IIB supergravity arising as near-horizon geometries of D1-F1-D3-D5-NS5-D7 brane intersections preserving 4 supersymmetries. We show that a subclass of these solutions asymptotes locally to the $\text{AdS}_6\times S^2\times \Sigma_2$ solution to Type IIB supergravity holographically dual to the five dimensional Sp(N) fixed point theory. This suggests that these solutions can be interpreted as D1-F1-D3 line defects within this CFT. Switching off the D7-branes, we act with $\text{SL}(2, \mathbb{R})$ to construct a second family of solutions that can be related to an $\text{AdS}_3\times S^3\times S^3$ class of M-theory backgrounds describing surface defects within the six dimensional (1,0) SCFT dual to $\text{AdS}_7/\mathbb{Z}_k\times S^4$. Finally, using non-Abelian T-duality we construct new classes of $\text{AdS}_2\times S^2\times S^2$ solutions to Type IIA supergravity with 4 supercharges and elaborate on their M-theory origin.

Negative Rényi entropy and brane intersection

In this work, we revisit the calculation of Rényi entropy in AdS3/(B)CFT2. We find that gravity solutions with brane intersection will lead to negative Rényi entropy.

The final model building for the supersymmetric Pati–Salam models from intersecting D6-branes

All the possible three-family {mathcal N}=1 supersymmetric Pati–Salam models constructed with intersecting D6-branes from Type IIA orientifolds on T^6/(mathbb {Z}_2times mathbb {Z}_2) are recently presented in arXiv:2112.09632. Taking models with largest wrapping number 5 and approximate gauge coupling unification at GUT scale as examples, we show string scale gauge coupling unification can be realized through two-loop renormalization group equation running by introducing seven pairs of vector-like particles from {mathcal N}=2 sector. The number of these introduced vector-like particles are fully determined by the brane intersection numbers while there are two D6-brane parallel to each other along one two-torus. We expect this will solve the gauge coupling unification problem in the generic intersecting brane worlds by introducing vector-like particles that naturally included in the {mathcal N}=2 sector.

Higgs Branches of rank-0 5d theories from M-theory on (Aj, Al) and (Ak, Dn) singularities

We study the dynamics of M-theory on isolated non-toric Calabi-Yau threefold singularities of type (Aj, Al) and (Ak, Dn), engineering five-dimensional rank-zero SCFTs. Our approach consists in mapping these backgrounds to type IIA string theory with D6 branes at angles and O6− planes, computing the five-dimensional open string modes located at the brane intersections. This permits us to characterize the Higgs Branches of these theories as algebraic varieties, determine the flavour and gauge group and inspect subtleties related to T-branes. Our methods apply for all the considered singularities: we give a closed formula for the (Aj, Al) Higgs Branches, and tables for the Higgs Branches of the (Ak, Dn) series.

Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams

We introduce a differential refinement of Cohomotopy cohomology theory, defined on Penrose diagram spacetimes, whose cocycle spaces are unordered configuration spaces of points. First we prove that brane charge quantization in this differential 4-Cohomotopy theory implies intersecting p/(p+2)-brane moduli given by ordered configurations of points in the transversal 3-space. Then we show that the higher (co-)observables on these brane moduli, conceived as the (co-)homology of the Cohomotopy cocycle space, are given by weight systems on horizontal chord diagrams and reflect a multitude of effects expected in the microscopic quantum theory of Dp/D(p+2)-brane intersections: condensation to stacks of coincident branes and their Chan-Paton factors, BMN matrix model and fuzzy funnel states, M2-brane 3-algebras, the Hanany-Witten rules, AdS3-gravity observables, supersymmetric indices of Coulomb branches as well as gauge/gravity duality between all these. We discuss this in the context of the hypothesis that the M-theory C-field is charge-quantized in Cohomotopy theory.

Miura operators, degenerate fields and the M2-M5 intersection

We determine the mathematical structures which govern the Ω deformation of supersymmetric intersections of M2 and M5 branes. We find that the supersymmetric intersections govern many aspects of the theory of W-algebras, including degenerate modules, the Miura transform and Coulomb gas constructions. We give an algebraic interpretation of the Pandharipande-Thomas box counting in ℂ3.

Warm Dark Matter from Higher-Dimensional Gauge Theories

Warm dark matter particles with masses in the keV range have been linked with the large group representations in gauge theories through a high number of species at decoupling. In this paper, we address WDM fermionic degrees of freedom from such representations. Bridging higher-dimensional particle physics theories with cosmology studies and astrophysical observations, our approach is two-folded, i.e., it includes realistic models from higher-dimensional representations and constraints from simulations tested against observations. Starting with superalgebras in exceptional periodicity theories, we discuss several symmetry reductions and we consider several representations that accommodate a high number of degrees of freedom. We isolate a model that naturally accommodates both the standard model representation and the fermionic dark matter in agreement with both large and small-scale constraints. This model considers an intersection of branes in D = 27 + 3 in a manner that provides the degrees of freedom for the standard model on one hand and 2048 fermionic degrees of freedom for dark matter, corresponding to a ∼2 keV particle mass, on the other. In this context, we discuss the theoretical implications and the observable predictions.

New AdS2 supergravity duals of 4d SCFTs with defects

We construct new families of AdS2× S2× S2 solutions with 4 supercharges in Type II supergravities. We show that subclasses of these solutions can be interpreted in terms of defect branes embedded in 4d mathcal{N} = 4 SYM, or orbifolds thereof. This is explicitly realised by showing that the solutions asymptote locally to AdS5× S5/ℤn, in Type IIB, or its T-dual background, in Type IIA. The latter is a Gaiotto-Maldacena geometry realised on an intersection of D4 and NS5 branes. We extend the Type IIA solutions to include D6 branes, and interpret them as describing backreacted baryon vertices within 4d mathcal{N} = 2 CFTs living in D4-NS5-D6 intersections. We propose explicit quiver quantum mechanics in which the defect branes play the role of colour branes, with the D4 branes of the D4-NS5-D6 intersection becoming flavour branes. These quivers are used to compute the degeneracies of the ground states of the dual super conformal quantum mechanics, that are shown to agree with the holographic expressions.

AdS2 geometries and non-Abelian T-duality in non-compact spaces

We obtain an AdS2 solution to Type IIA supergravity with 4 Poincaré supersymmetries, via non-Abelian T-duality with respect to a freely acting SL(2,R) isometry group, operating on the AdS3×S3×CY2 solution to Type IIB. That is, non-Abelian T-duality on AdS3. The dual background obtained fits in the class of AdS2×S3×CY2 solutions to massive Type IIA constructed in [1]. We propose and study a quiver quantum mechanics dual to this solution that we interpret as describing the backreaction of the baryon vertex of a D4-D8 brane intersection.

New IIB intersecting brane solutions yielding supersymmetric AdS3 vacua

We consider different (supersymmetric) brane intersections in type IIB string theory that preserve (1 + 1)D Lorentz symmetry. We provide the full supergravity solutions in their analytic form and discuss their physical properties. The Ansatz for the spacetime dependence of the different brane warp factors goes beyond the harmonic superposition principle. By studying the associated near-horizon geometry, we construct interesting classes of AdS3 vacua in type IIB and highlight their relation to the existing classifications in the literature. Finally, we discuss their holographic properties.

Q-deformation of corner vertex operator algebras by Miura transformation

Recently, Gaiotto and Rapcak proposed a generalization of WN algebra by considering the symmetry at the corner of the brane intersection (corner vertex operator algebra). The algebra, denoted as YL,M,N, is characterized by three non-negative integers L, M, N. It has a manifest triality automorphism which interchanges L, M, N, and can be obtained as a reduction of W1+∞ algebra with a “pit” in the plane partition representation. Later, Prochazka and Rapcak proposed a representation of YL,M,N in terms of L + M + N free bosons by a generalization of Miura transformation, where they use the fractional power differential operators.In this paper, we derive a q-deformation of the Miura transformation. It gives a free field representation for q-deformed YL,M,N, which is obtained as a reduction of the quantum toroidal algebra. We find that the q-deformed version has a “simpler” structure than the original one because of the Miki duality in the quantum toroidal algebra. For instance, one can find a direct correspondence between the operators obtained by the Miura transformation and those of the quantum toroidal algebra. Furthermore, we can show that the both algebras share the same screening operators.

Fermions and baryons as open-string states from brane junctions

There has been recent progress towards understanding the dynamics of world-volume fermions that arise as open-string modes from brane intersections in the probe limit (Nf/Nc → 0). In this work we consider all possible BPS brane junctions in Type IIA/B supergravity theories. We study in detail the dynamics of these states by deriving their equations of motion. We show the expected degeneracy of the bosonic and fermionic fluctuations as is expected due to the preserved supersymmetry. We also give some supporting evidence and refine the notion that these states can effectively describe baryon operators in a certain regime of the field theory’s parameter space. Our piece of evidence is the demonstration of the expected scaling of the mass in the large-Nc limit of the theory for these fermionic states; M2 ∼ {N}_c^2 . Finally, we explain analytically the avoided level crossing that was observed in a previous work after the inclusion of higher dimension operators in the field theory.

Searching for surface defect CFTs within AdS3

We study AdS3 times {S}^3/{mathrm{mathbb{Z}}}_ktimes {tilde{S}}^3/{mathrm{mathbb{Z}}}_{k^{prime }} solutions to M-theory preserving mathcal{N} = (0, 4) supersymmetries, arising as near-horizon limits of M2-M5 brane intersections ending on M5’-branes, with both types of five-branes placed on A-type singularities. Solutions in this class asymptote locally to AdS7 /{mathrm{mathbb{Z}}}_ktimes {tilde{S}}^3/{mathrm{mathbb{Z}}}_{k^{prime }} , and can thus be interpreted as holographic duals to surface defect CFTs within the mathcal{N} = (1, 0) 6d CFT dual to this solution. Upon reduction to Type IIA, we obtain a new class of solutions of the form AdS3× S3/ℤk× S2×Σ2 preserving (0,4) supersymmetries. We construct explicit 2d quiver CFTs dual to these solutions, describing D2-D4 surface defects embedded within the 6d (1,0) quiver CFT dual to the AdS7/ℤk solution to massless IIA. Finally, in the massive case, we show that the recently constructed AdS3× S2× CY2 solutions with mathcal{N} = (0, 4) supersymmetries gain a defect interpretation as surface CFTs originating from D2-NS5-D6 defects embedded within the 5d CFT dual to the Brandhuber-Oz AdS6 background.

Holographic description of M-branes via AdS2

We study AdS2× S4× S2× Σ2 solutions in type IIB string theory arising from D1-D3-NS5 brane intersections. These backgrounds enjoy sixteen supercharges and the corresponding internal geometry is non-compact due to the specific form of the warping w.r.t. the Riemann surface Σ2. Even though a direct computation of the holographic free energy of the would-be dual CFT1 yields a divergent behaviour, it reveals the typical N3 scaling of a 6d theory upon introducing a hard cut-off. We claim that such geometries may be interpreted as the gravity duals of M(atrix) models describing an IR phase of the (2, 0) theory of M5 branes, in presence of momentum and NUT charges. We discuss parallel AdS2 geometries describing longitudinal M2 branes in the UV, where the counting of the number of degrees of freedom correctly reproduces the expected N3/2 behaviour of the dual field theory. These geometries provide explicit examples where deconstructed extra dimensions yield well-defined UV descriptions in terms of higher-dimensional CFTs.

Special holonomy manifolds, domain walls, intersecting branes and T-folds

We discuss the special holonomy metrics of Gibbons, Lu, Pope and Stelle, which were constructed as nilmanifold bundles over a line by uplifting supersymmetric domain wall solutions of supergravity to 11 dimensions. We show that these are dual to intersecting brane solutions, and considering these leads us to a more general class of special holonomy metrics. Further dualities relate these to non-geometric backgrounds involving intersections of branes and exotic branes. We discuss the possibility of resolving these spaces to give smooth special holonomy manifolds.

AdS2 solutions and their massive IIA origin

We consider warped AdS2 × ℳ4 backgrounds within F(4) gauged supergravity in six dimensions. In particular, we are able to find supersymmetric solutions of the aforementioned type characterized by AdS6 asymptotics and an ℳ4 given by a three-sphere warped over a segment. Subsequently, we provide the 10D uplift of the solutions to massive type IIA supergravity, where the geometry is AdS2 × S3 × {tilde{S}}^3 warped over a strip. Finally we construct the brane intersection underlying one of these supergravity backgrounds. The explicit setup involves a D0-F1-D4 bound state intersecting a D4-D8 system.