46 research outputs found

### Topological Model for Domain Walls in (Super-)Yang-Mills Theories

We derive a topological action that describes the confining phase of
(Super-)Yang-Mills theories with gauge group $SU(N)$, similar to the work
recently carried out by Seiberg and collaborators. It encodes all the
Aharonov-Bohm phases of the possible non-local operators and phases generated
by the intersection of flux tubes. Within this topological framework we show
that the worldvolume theory of domain walls contains a Chern-Simons term at
level $N$ also seen in string theory constructions. The discussion can also
illuminate dynamical differences of domain walls in the supersymmetric and
non-supersymmetric framework. Two further analogies, to string theory and the
fractional quantum Hall effect might lead to additional possibilities to
investigate the dynamics

### The Toric SO(10) F-Theory Landscape

Supergravity theories in more than four dimensions with grand unified gauge
symmetries are an important intermediate step towards the ultraviolet
completion of the Standard Model in string theory. Using toric geometry, we
classify and analyze six-dimensional F-theory vacua with gauge group SO(10)
taking into account Mordell-Weil U(1) and discrete gauge factors. We determine
the full matter spectrum of these models, including charged and neutral SO(10)
singlets. Based solely on the geometry, we compute all matter multiplicities
and confirm the cancellation of gauge and gravitational anomalies independent
of the base space. Particular emphasis is put on symmetry enhancements at the
loci of matter fields and to the frequent appearance of superconformal points.
They are linked to non-toric K\"ahler deformations which contribute to the
counting of degrees of freedom. We compute the anomaly coefficients for these
theories as well by using a base-independent blow-up procedure and
superconformal matter transitions. Finally, we identify six-dimensional
supergravity models which can yield the Standard Model with high-scale
supersymmetry by further compactification to four dimensions in an Abelian flux
background.Comment: 64 pages, 40 pages appendices, 18 figures, 6 Tables, references
added, published versio

### The Fate of Discrete 1-Form Symmetries in 6d

Recently introduced generalized global symmetries have been useful in order
to understand non-perturbative aspects of quantum field theories in four and
lower dimensions. In this paper we focus on 1-form symmetries of weakly coupled
6d supersymmetric gauge theories coupled to tensor multiplets. We study their
interplay with large gauge transformations for dynamical tensor fields. In a
non-trivial background for the global 1-form symmetry, this leads to an
ambiguity of the effective field theory partition function. This anomaly is
eliminated by the inclusion of BPS strings. However, the non-trivial 1-form
background can induce fractional string charges which are not compatible with
Dirac quantization, and hence the symmetry is absent. The anomalous term
therefore serves as a tool to detect whether the discrete 1-form symmetries are
realized, which we demonstrate in explicit examples originating from string
compactifications. We also corroborate this by finding that a non-trivial
ambiguity is related to states which explicitly break the global 1-form
symmetry, which appear as generally massive excitations of the 6d BPS strings.
For 6d theories consistently coupled to gravity, this ambiguity of the
partition function hints at the presence of a symmetry breaking tower of
states. When the ambiguity is absent, the F-theory realization of the theories
points to the gauging of the 1-form symmetries via the presence of non-trivial
Mordell--Weil torsion.Comment: 46 pages + appendices, 2 figures; v2: typos corrected, references
adde

### The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings

We study global anomalies of discrete gauge symmetries in six-dimensional
supergravities and their realizations in F-theory. We explicitly construct a
discrete Green-Schwarz mechanism that depends on the choice of a coupling
constant and on a certain quadratic refinement in differential cohomology. By
geometrically engineering theories with $G=\mathbb{Z}_3$ gauge symmetry and no
tensor multiplets, we observe that a particular choice of the quadratic
refinement is singled out in F-theory. This implies new Swampland constraints
on the discrete charge spectra of 6d supergravities. On the other hand, the
discrete Green-Schwarz coupling depends on the geometry of the Calabi-Yau. We
use anomaly inflow to relate this to a 't Hooft anomaly of the induced global
symmetry in the worldsheet theories of non-critical strings. Using topological
symmetry lines, we further relate this anomaly to the modular properties of
twisted-twined elliptic genera. We then argue that the latter are encoded in
the A-model topological string partition functions on different torus
fibrations that are equipped with a flat torsional B-field. This allows us to
derive a geometric expression for the global discrete anomaly in terms of the
height-pairing of a multi-section on a genus one fibered Calabi-Yau.Comment: 35+16 pages, 21 figure

### Gauge group topology of 8D Chaudhuri-Hockney-Lykken vacua

Compactifications of the Chaudhuri-Hockney-Lykken (CHL) string to eight dimensions can be characterized by embeddings of root lattices into the rank 12 momentum lattice Lambda(M), the so-called Mikhailov lattice. Based on these data, we devise a method to determine the global gauge group structure including all U(1) factors. The key observation is that, while the physical states correspond to vectors in the momentum lattice, the gauge group topology is encoded in its dual. Interpreting a nontrivial pi(1)(G) = Z for the non-Abelian gauge group G as having gauged a Z 1-form symmetry, we also prove that all CHL gauge groups are free of a certain anomaly [1] that would obstruct this gauging. We verify this by explicitly computing Z for all 8D CHL vacua with rank(G) = 10. Since our method applies also to T-2 compactifications of heterotic strings, we further establish a map that determines any CHL gauge group topology from that of a "parent" heterotic model

### IIB Explored: Reflection 7-Branes

The Swampland Cobordism Conjecture successfully predicts the supersymmetric
spectrum of 7-branes of IIB / F-theory. Including reflections on the F-theory
torus, it also predicts the existence of new non-supersymmetric objects, which
we dub reflection 7-branes (R7-branes). We present evidence that these
R7-branes only exist at strong coupling. R7-branes serve as end of the world
branes for 9D theories obtained from type IIB asymmetric orbifold and
Dabholkar-Park orientifold backgrounds, and an anomaly inflow analysis suggests
the existence of a gapless Weyl fermion, which would have the quantum numbers
of a goldstino. Using general arguments, we conclude that different kinds of
branes are able to end on the R7, and accounting for their charge requires
exotic localized degrees of freedom, for which the simplest possibility is a
massless 3-form field on the R7-brane worldvolume. We also show how to
generalize the standard F-theory formalism to account for reflections.Comment: 44 pages, 3 figure

### Chiral fermions and anomaly cancellation on orbifolds with Wilson lines and flux

We consider six-dimensional supergravity compactified on orbifolds with
Wilson lines and bulk flux. Torus Wilson lines are decomposed into Wilson lines
around the orbifold fixed points, and twisted boundary conditions of matter
fields are related to fractional localized flux. Both, orbifold singularities
and flux lead to chiral fermions in four dimensions. We show that in addition
to the standard bulk and fixed point anomalies the Green-Schwarz term also
cancels the four-dimensional anomaly induced by the flux background. The two
axions contained in the antisymmetric tensor field both contribute to the
cancellation of the four-dimensional anomaly and the generation of a vector
boson mass via the Stueckelberg mechanism. An orthogonal linear combination of
the axions remains massless and couples to the gauge field in the standard way.
Furthermore, we construct convenient expressions for the wave functions of the
zero modes and relate their multiplicity and behavior at the fixed points to
the bulk flux quanta and the Wilson lines.Comment: 30 pages, 4 figures, 1 table, clarifying remarks adde