We explore how quantum gravity effects, manifested through the breaking of discrete symmetry responsible for both dark matter and domain walls, can have observational effects cosmic microwave background observations gravitational waves. To illustrate idea we consider a simple model with two scalar fields ${\mathcal{Z}}_{2}$ symmetries, one being stability, other spontaneously broken where symmetries are assumed to be explicitly by effects. show recent wave spectrum observed several pulsar...

We compute the 4d superconformal index for N=1,2 gauge theories on S^1 x L(p,1), where L(p,1) is a lens space. find that reduces to 3d N=2,4 S^2 in large p limit, and partition function squashed when size of temporal shrinks zero. As an application our index, we study N=2 field arising from 6d N=(2,0) A_1 theory punctured Riemann surface, conjecture existence 2d Topological Quantum Field Theory surface whose correlation coincides with L(p,1).

Starting with a four-dimensional gauge theory approach to rational, elliptic, and trigonometric solutions of the Yang-Baxter equation, we determine corresponding quantum group deformations all orders in $\hbar$ by deducing their RTT presentations. The arguments give are mix familiar ones reasoning that is more transparent from point view. apply most directly for $\mathfrak{gl}_N$ can be extended simple Lie algebras other than $\mathfrak{e}_8$ taking into account self-duality some...

Several years ago, it was proposed that the usual solutions of Yang-Baxter equation associated to Lie groups can be deduced in a systematic way from fourdimensional gauge theory.In present paper, we extend this picture, fill many details, and arguments concrete down-to-earth way.Many interesting effects, including leading nontrivial contributions Rmatrix, operator product expansion line operators, framing anomaly, quantum deformation leads g[[z]] Yangian, are computed explicitly via Feynman...

In the context of conformal field theories in general space-time dimension, we find all possible singularities blocks as functions scaling dimension Δ exchanged operator. particular, argue, using representation theory parabolic Verma modules, that odd spacetime are only simple poles. We discuss how to use this information write recursion relations determine blocks. first recover relation introduced [1] for external scalar operators. then generalize associated four point function three and...

A low-energy effective theory is said to be in the swampland if it does not have any consistent UV completion inside a of quantum gravity. The natural question standard model particle physics, possibly with some minimal extensions, are or not. We discuss this view recent conjectures. prove no-go theorem concerning modification Higgs sector. Moreover, we find that QCD axion incompatible conjectures, unless sophisticated possibilities considered. implications result for spontaneous breaking CP...

We explore non-invertible symmetries in two-dimensional lattice models with subsystem $\mathbb Z_2$ symmetry. introduce a Z_2$-gauging procedure, called the Kramers-Wannier transformation, which generalizes ordinary transformation. The corresponding duality operators and defects are constructed by gaugings on whole or half of Hilbert space. By gauging twice, we derive fusion rules defects, enriches Ising features. Subsystem mobile both spatial directions, unlike invertible symmetries....

Abstract We review recent developments in the theory of brane tilings and four‐dimensional 𝒩 = 1 supersymmetric quiver gauge theories. This consists two parts. In part I, we describe foundations tilings, emphasizing physical interpretation as fivebrane systems. II, discuss application to AdS/CFT correspondence homological mirror symmetry. More topics, such orientifold phenomenological model building, similarities with BPS solitons theories, are also briefly discussed. paper is a revised...

We report on the exact computation of S^3 partition function U(N)_k\times U(N)_{-k} ABJM theory for k=1, N=1,...,19. The result is a polynomial in \pi^{-1} with rational coefficients. As an application our results we numerically determine coefficient membrane 1-instanton correction to function.

A bstract The quiver Yangian, an infinite-dimensional algebra introduced recently in [1], is the underlying BPS state counting problems for toric Calabi-Yau three-folds. We introduce trigonometric and elliptic analogues of Yangians, which we call toroidal algebras algebras, respectively. construct representations shifted terms statistical model crystal melting. also derive their from equivariant localization three-dimensional $$ \mathcal{N} <mml:math...

In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of 6d (2, 0) theory type A N −1 on a 3-manifold M . The so-called 3d-3d correspondence is relation between complexified Chern-Simons (with gauge group $$ \mathrm{S}\mathrm{L}\left(N,\mathbb{C}\right) ) 3d \mathcal{N}=2 T [M ]. We presence defects, which are knots/links inside 3-manifold. Our employs number different methods: state-integral models for complex theory, cluster algebra techniques, domain...

We study two-dimensional integrable field theories from the viewpoint of four-dimensional Chern-Simons-type gauge theory introduced recently. The are realized as effective for coupled with surface defects, and we can systematically compute their Lagrangians Lax operators satisfying zero-curvature condition. Our construction includes many known theories, such Gross-Neveu models, principal chiral models Wess-Zumino terms symmetric-space coset sigma models. Moreover obtain various...

We discuss phenomenological consequences of the recently introduced refinements de Sitter swampland conjecture, which constrains first and second derivative scalar potential in terms two $O(1)$ constants $c$ ${c}^{\ensuremath{'}}$. Contrary to original refinement has no constraints on spontaneous breaking scenarios, such as Higgs, chiral symmetry breaking, QCD axion. However, still strongly inflation models. While we can achieve sufficient number e-foldings, single-field inflationary models...

We discuss ensemble averages of two-dimensional conformal field theories associated with an arbitrary indefinite lattice integral quadratic form $Q$. provide evidence that the holographic dual after average is three-dimensional Abelian Chern-Simons theory kinetic term determined by The resulting partition function can be written as a modular form, expressed sum over functions on lens spaces. For odd lattices, bulk spin theory, and we identify several novel phenomena in this case. also...

We explore an exact duality in $(2+1)$d between the fermionization of a bosonic theory with $\mathbb{Z}_2$ subsystem symmetry and fermionic fermion parity symmetry. A typical example is plaquette Ising model model. first revisit standard boson-fermion $(1+1)$d 0-from symmetry, presenting way generalizable to $(2+1)$d. proceed establish on lattice by using generalized Jordan-Wigner map, careful discussion mapping twist sectors. This motivates us introduce Arf invariant, which exhibits...

When simulating the time evolution of quantum many-body systems on a digital computer, one faces challenges noise and Trotter error due to discretization. The in integrable spin chains can be under control if discrete preserves integrability. In this work we implement, real computer classical simulators, Trotterization spin-1/2 Heisenberg XXX chain. We study how affects several conserved charges, observe decay expectation values. addition early behaviors evolution, which potentially used...

The gravitational positivity bound gives quantitative “swampland” constraints on low-energy effective theories inside of quantum gravity. We give a comprehensive discussion this for those interested in applications to phenomenological model building. present practical recipe deriving the bound, and discuss subtleties relevant realistic models. As an illustration, we study scattering massive gauge bosons Higgs/Stückelberg mechanism. Under certain assumptions amplitudes at high energy, obtain...

We construct statistical mechanical models of crystal melting describing the flavoured Witten indices $\mathcal{N}\ge 2$ supersymmetric quiver gauge theories. Our results can be derived from Jeffrey-Kirwan (JK) residue formulas, and generalize previous for quivers corresponding to toric Calabi-Yau threefolds fourfolds a large class satisfying no-overlap condition, including those some non-toric manifolds. new algebras which we call double Yangians/algebras, as well their representations in...