<p>The U-dualities of maximally supersymmetric nonchiral supergravity (SUGRA) theories lead to strong constraints on the nonperturbative structure of quantum gravity. In this paper, we determine spin- and pin-lifts of these dualities, which extend this action to fermionic degrees of freedom. Among other things, this allows us to access nonsupersymmetric sectors of these low energy effective field theories in which bosonic and fermionic degrees of freedom are treated differently. We use this refinement of the duality groups, in tandem with the Swampland cobordism conjecture, to predict new codimension-two branes. These are a natural generalization of the recently discovered R7-branes of type II string theories. The first bordism groups for Spin-twisted duality bundles that follow directly from the Abelianization of the duality groups. Viewing the SUGRA theory as the low energy limit of a toroidal compactification of M-theory, winding around these codimension-two defects enacts a reflection around one of the torus directions, which, in the effective field theory, appears as a charge conjugation symmetry. We establish some basic properties of such branes, including determining Bogomol’nyi-Prasad-Sommerfield objects which can end on it, as well as braiding rules and bound states realized by multiple reflection branes.</p>

United States

Vivek Chakrabhavi

Arun Debray

CERN

Markus Dierigl

Jonathan J. Heckman

Reflection branes, bordisms, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi></math> dualities

We study defects in symmetry breaking phases, such as domain walls, vortices, and hedgehogs. In particular, we focus on the localized gapless excitations which sometimes occur at the cores of these objects. These are topologically protected by an ’t Hooft anomaly. We classify different symmetry breaking phases in terms of the anomalies of these defects, and relate them to the anomaly of the broken symmetry by an anomaly-matching formula. We also derive the obstruction to the existence of a symmetry breaking phase with a local defect. We obtain these results using a long exact sequence of groups of invertible field theories, which we call the “symmetry breaking long exact sequence” (SBLES). The mathematical backbone of the SBLES is studied in a companion paper [1]. Our work further develops the theory of higher Berry phase and its bulk-boundary correspondence, and serves as a new computational tool for classifying symmetry protected topological phases.

Sanath Devalapurkar

Cameron Krulewski

Yu Liu

Natalia Pacheco-Tallaj

Ryan Thorngren

A long exact sequence in symmetry breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases

The three tachyon-free non-supersymmetric string theories in ten dimensions provide a handle on quantum gravity away from the supersymmetric lamppost. However, they have not been shown to be fully consistent; although local anomalies cancel due to versions of the Green-Schwarz mechanism, there could be global anomalies, not cancelled by the Green-Schwarz mechanism, that could become fatal pathologies. We compute the twisted string bordism groups that control these anomalies via the Adams spectral sequence, showing that they vanish completely in two out of three cases (Sugimoto and SO(16)2) and showing a partial vanishing also in the third (Sagnotti 0’B model). We also compute lower-dimensional bordism groups of the non-supersymmetric string theories, which are of interest to the classification of branes in these theories via the Cobordism Conjecture. We propose a worldvolume content based on anomaly inflow for the SO(16)2 NS5-brane, and discuss subtleties related to the torsion part of the Bianchi identity. As a byproduct of our techniques and analysis, we also reprove that the outer ℤ2 automorphism swapping the two E 8 factors in the supersymmetric heterotic string is also non-anomalous.

Germany

Ivano Basile

Spain

Matilda Delgado

Miguel Montero

Global anomalies &amp; bordism of non-supersymmetric strings

2-group symmetries arise in physics when a 0-form symmetry G [0] and a 1-form symmetry H [1] intertwine, forming a generalised group-like structure. Specialising to the case where both G [0] and H [1] are compact, connected, abelian groups (i.e. tori), we analyse anomalies in such ‘toric 2-group symmetries’ using the cobordism classification. As a warm up example, we use cobordism to study various ’t Hooft anomalies (and the phases to which they are dual) in Maxwell theory defined on non-spin manifolds. For our main example, we compute the 5th spin bordism group of B|𝔾| where 𝔾 is any 2-group whose 0-form and 1-form symmetry parts are both U(1), and |𝔾| is the geometric realisation of the nerve of the 2-group 𝔾. By leveraging a variety of algebraic methods, we show that   <math> <msubsup> <mi>Ω</mi> <mn>5</mn> <mtext>Spin</mtext> </msubsup> <mfenced> <mrow> <mi>B</mi> <mfenced> <mi>G</mi> </mfenced> </mrow> </mfenced> <mo>≅</mo> <mi>ℤ</mi> <mo>/</mo> <mi>m</mi> </math>  $$ {\varOmega}_5^{\textrm{Spin}}\left(B\left|\mathbbm{G}\right|\right)\cong \mathbb{Z}/m $$  where m is the modulus of the Postnikov class for 𝔾, and we reproduce the expected physics result for anomalies in 2-group symmetries that appear in 4d QED. Moving down two dimensions, we recap that any (anomalous) U(1) global symmetry in 2d can be enhanced to a toric 2-group symmetry, before showing that its associated local anomaly reduces to at most an order 2 anomaly, when the theory is defined with a spin structure.