We study the anomalies of two-dimensional BPS defects in six-dimensional $$ \mathcal{N} $$ = (1 0) superconformal field theories. Using a holographic description of these defects furnished by probe D4-branes in AdS solutions of ten-dimensional type IIA supergravity, we compute the two independent defect Weyl anomalies from the on-shell action for a spherical defect and defect sphere entanglement entropy. We find agreement between the holographic prediction for the defect A-type anomaly coming from the defect sphere free energy and the leading large contribution to the defect ’t Hooft anomaly found using anomaly inflow. We also find agreement between the holographic computation of the expectation value of a surface operator wrapping a torus and the supersymmetric localization computation for a circular Wilson loop in $$ \mathcal{N} $$ = 1 super Yang-Mills theory on . Lastly, we holographically compute the defect gravitational anomaly from the Wess-Zumino action of the probe D4-brane, which provides a subleading large correction to the defect A-type anomaly.

Italy

Fabio Apruzzi

Thailand

Noppadol Mekareeya

Brandon Robinson

Alessandro Tomasiello

Superconformal anomalies for string defects in six-dimensional

Finsler geometry is a natural generalization of (pseudo-)Riemannian geometry, where the line element is not the square root of a quadratic form but a more general homogeneous function. Parameterizing this in terms of symmetric tensors suggests a possible interpretation in terms of higher-spin fields. We will see here that, at linear level in these fields, the Finsler version of the Ricci tensor leads to the curved-space Fronsdal equation for all spins, plus a Stueckelberg-like coupling. Nonlinear terms can also be systematically analyzed, suggesting a possible interacting structure. No particular choice of spacetime dimension is needed. The Stueckelberg mechanism breaks gauge transformations to a redundancy that does not change the geometry. This creates a serious issue: non-transverse modes are not eliminated, at least for the versions of Finsler dynamics examined in this paper.

Higher spins and Finsler geometry

For the Laplacian of an n-Riemannian manifold X, the Weyl law states that the k-th eigenvalue is asymptotically proportional to (k/V)2/n , where V is the volume of X. We show that this result can be derived via physical considerations by demanding that the gravitational potential for a compactification on X behaves in the expected (4+n)-dimensional way at short distances. In simple product compactifications, when particle motion on X is ergodic, for large k the eigenfunctions oscillate around a constant, and the argument is relatively straightforward. The Weyl law thus allows to reconstruct the four-dimensional Planck mass from the asymptotics of the masses of the spin 2 Kaluza-Klein modes. For warped compactifications, a puzzle appears: the Weyl law still depends on the ordinary volume V, while the Planck mass famously depends on a weighted volume obtained as an integral of the warping function. We resolve this tension by arguing that in the ergodic case the eigenfunctions oscillate now around a power of the warping function rather than around a constant, a property that we call weighted quantum ergodicity. This has implications for the problem of gravity localization, which we discuss. We show that for spaces with Dp-brane singularities the spectrum is discrete only for p = 6, 7, 8, and for these cases we rigorously prove the Weyl law by applying modern techniques from RCD theory.

United States

G. Luca

Nicolò Ponti

United Kingdom

Andrea Mondino

Can you hear the Planck mass?

In models with extra dimensions, matter particles can be easily localized to a ‘brane world’, but gravitational attraction tends to spread out in the extra dimensions unless they are small. Strong warping gradients can help localize gravity closer to the brane. In this note we give a mathematically rigorous proof that the internal wave-function of the massless graviton is constant as an eigenfunction of the weighted Laplacian, and hence is a power of the warping as a bound state in an analogue Schrödinger potential. This holds even in presence of singularities induced by thin branes.

Harmonic functions and gravity localization

We introduce a class of 3d theories consisting of strongly-coupled   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 systems coupled to   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 3 Chern-Simons gauge multiplets, which exhibit   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 enhancements when a peculiar condition on the Chern-Simons levels is met. An example is the SU(N)3 Chern-Simons theory coupled to the 3d T  N  theory, which enhances to   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 when 1/k 1 + 1/k 2 + 1/k 3 = 0. We also show that some but not all of these   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 enhancements can be understood by considering M5-branes on a special class of Seifert manifolds. Our construction provides a large class of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 theories which have not been studied previously.

France

Benjamin Assel

Japan

Yuji Tachikawa

On   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 supersymmetry enhancements in three dimensions

Vacuum compactifications may suffer from instabilities under small perturbations or tunnel effects; both are difficult to analyze. In this paper we consider the issue from a higher-dimensional perspective. We first look at how stability works for supersymmetric vacua, where it is widely expected to hold. We first show that the nucleation of brane bubbles in type II AdS compactifications is forbidden in the probe approximation by a simple argument involving pure spinors and calibrations. We then adapt familiar positive-energy theorems directly to M-theory and type II supergravity, rather than to their effective lower-dimensional reductions, also showing how to consistently include localized sources. We finally initiate an analysis of how these arguments might be extended to non-supersymmetric vacua. In M-theory, at the lower-derivative level, we find that the most natural modifications fail to stabilize the skew-whiffed and Englert vacua.

Suvendu Giri

Luca Martucci

On the stability of string theory vacua

Warped AdS3 solutions in 10 dimensional supergravity that preserve   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = (1, 1) supersymmetry are considered. Sufficient geometric conditions for their existence, and to stop the AdS3 factor experiencing an enhancement to AdS4, are presented. The internal space of such solutions decomposes as a foliation of M6 over an interval where M6 supports either an SU(3)- or SU(2)-structure. The former case is classified in terms of torsion classes and new solutions are found.

Spain

Niall Macpherson

<math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = (1, 1) supersymmetric AdS3 in 10 dimensions

We consider gravity compactifications whose internal space consists of small bridges connecting larger manifolds, possibly noncompact. We prove that, under rather general assumptions, this leads to a massive spin-two field with very small mass. The argument involves a recently-noticed relation to Bakry-Émery geometry, a version of the so-called Cheeger constant, and the theory of synthetic Ricci lower bounds. The latter technique allows generalizations to non-smooth spaces such as those with D-brane singularities. For AdS d  vacua with a bridge admitting an AdS d+1 interpretation, the holographic dual is a CFT d  with two CFT d−1 boundaries. The ratio of their degrees of freedom gives the graviton mass, generalizing results obtained by Bachas and Lavdas for d = 4. We also prove new bounds on the higher eigenvalues. These are in agreement with the spin-two swampland conjecture in the regime where the background is scale-separated; in the opposite regime we provide examples where they are in naive tension with it.

Cheeger bounds on spin-two fields

In a broad class of gravity theories, the equations of motion for vacuum compactifications give a curvature bound on the Ricci tensor minus a multiple of the Hessian of the warping function. Using results in so-called Bakry-Émery geometry, we put rigorous general bounds on the KK scale in gravity compactifications in terms of the reduced Planck mass or the internal diameter. We reexamine in this light the local behavior in type IIA for the class of supersymmetric solutions most promising for scale separation. We find that the local O6-plane behavior cannot be smoothed out as in other local examples; it generically turns into a formal partially smeared O4.

Leaps and bounds towards scale separation

We study subleading corrections to the genus-zero free energy of the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 3 Gaiotto-Tomasiello theory. In general, we obtain the endpoints and free energy as a set of parametric equations via contour integrals of the planar resolvent, up to exponentially suppressed corrections. In the particular case that the two gauge groups in the quiver are of equal rank, we find an explicit (perturbative) expansion for the free energy. If, additionally, both groups have equal levels, then we find the full expression for the genus-zero free energy, modulo exponentially suppressed corrections. We also verify our results numerically.