scholarly journals Kostant Pairs of Lie Type and Conformal Embeddings

2019 ◽  
pp. 1-22 ◽  
Author(s):  
Dražen Adamović ◽  
Victor G. Kac ◽  
Pierluigi Möseneder Frajria ◽  
Paolo Papi ◽  
Ozren Perše
Keyword(s):  
Conformal Embeddings

Quantum fluctuations of the metric, three-geometries and conformal embeddings in four-manifolds

2021 ◽  
Author(s):  
Simon Davis
Keyword(s):  
Path Integrals ◽  
Invariance Group ◽  
Two Dimensional ◽  
Four Dimensions ◽  
Physical Conditions ◽  
Exponential Expansion ◽  
Cotangent Bundles ◽  
Four Manifolds ◽  
Conformal Embeddings ◽  
Natural Relation

In this paper, connections between the path integrals for four-dimensional quantum gravity and string theory are emphasized. It is shown that there is a natural relation between these two path integrals based on the theorems on embeddings of two-dimensional surfaces in four dimensions and four-dimensional manifolds in ten dimensions. The isometry groups of the three-geometries that are spatial hypersurfaces confomally embedded in the four-manifolds are required to be subgroups of [Formula: see text], which is the invariance group of the Pfaffian differential system satisfied by one form in the cotangent bundles on the four-manifolds. Based on this and other physical conditions, the three-geometries are restricted to be [Formula: see text], [Formula: see text] and [Formula: see text] with a boundary, which may be included in the quantum gravitational path integral over four-manifolds which are closed at initial times followed by an exponential expansion compatible with supersymmetry.

scholarly journals Conformal embeddings and higher-spin bulk duals

2017 ◽  
Vol 95 (6) ◽  
Author(s):  
Dushyant Kumar ◽  
Menika Sharma
Keyword(s):  
Higher Spin ◽  
Conformal Embeddings

scholarly journals Finite vs. Infinite Decompositions in Conformal Embeddings

2016 ◽  
Vol 348 (2) ◽  
pp. 445-473 ◽  
Author(s):  
Dražen Adamović ◽  
Victor G. Kac ◽  
Pierluigi Möseneder Frajria ◽  
Paolo Papi ◽  
Ozren Perše
Keyword(s):  
Conformal Embeddings

scholarly journals Conformal embeddings of affine vertex algebras in minimal W-algebras II: decompositions

2017 ◽  
Vol 12 (2) ◽  
pp. 261-315 ◽  
Author(s):  
Dražen Adamović ◽  
Victor G. Kac ◽  
Pierluigi Möseneder Frajria ◽  
Paolo Papi ◽  
Ozren Perše
Keyword(s):  
Vertex Algebras ◽  
Conformal Embeddings

scholarly journals Exceptional Chern-Simons-Matter dualities

2019 ◽  
Vol 7 (4) ◽  
Author(s):  
Clay Cordova ◽  
Po-Shen Hsin ◽  
Kantaro Ohmori
Keyword(s):  
Gauge Theory ◽  
Topological Field Theories ◽  
Time Reversal ◽  
Three Dimensional ◽  
Field Theories ◽  
Chiral Algebra ◽  
Gauge Groups ◽  
Topological Field ◽  
Conformal Embeddings ◽  
Chern Simons

We use conformal embeddings involving exceptional affine Kac-Moody algebras to derive new dualities of three-dimensional topological field theories. These generalize the familiar level-rank duality of Chern-Simons theories based on classical gauge groups to the setting of exceptional gauge groups. For instance, one duality sequence we discuss is (E_{N})_{1}\leftrightarrow SU(9-N)_{-1}(EN)1↔SU(9−N)−1. Others such as SO(3)_{8}\leftrightarrow PSU(3)_{-6},SO(3)8↔PSU(3)−6, are dualities among theories with classical gauge groups that arise due to their embedding into an exceptional chiral algebra. We apply these equivalences between topological field theories to conjecture new boson-boson Chern-Simons-matter dualities. We also use them to determine candidate phase diagrams of time-reversal invariant G_{2}G2 gauge theory coupled to either an adjoint fermion, or two fundamental fermions.

scholarly journals On the classification of non-equal rank affine conformal embeddings and applications

2018 ◽  
Vol 24 (3) ◽  
pp. 2455-2498 ◽  
Author(s):  
Dražen Adamović ◽  
Victor G. Kac ◽  
Pierluigi Möseneder Frajria ◽  
Paolo Papi ◽  
Ozren Perše
Keyword(s):  
Conformal Embeddings

scholarly journals Branching rules for conformal embeddings

1995 ◽  
Vol 173 (1) ◽  
pp. 1-16 ◽  
Author(s):  
F. Levstein ◽  
J. I. Liberati
Keyword(s):  
Branching Rules ◽  
Conformal Embeddings

scholarly journals An Application of Collapsing Levels to the Representation Theory of Affine Vertex Algebras

2018 ◽  
Vol 2020 (13) ◽  
pp. 4103-4143 ◽  
Author(s):  
Dražen Adamović ◽  
Victor G Kac ◽  
Pierluigi Möseneder Frajria ◽  
Paolo Papi ◽  
Ozren Perše
Keyword(s):  
Maximal Ideal ◽  
Vertex Algebra ◽  
Lie Superalgebras ◽  
Vertex Algebras ◽  
Locally Finite ◽  
Complete Reducibility ◽  
Finite Module ◽  
Nontrivial Ideal ◽  
Conformal Embeddings ◽  
Reducibility Result

Abstract We discover a large class of simple affine vertex algebras $V_{k} ({\mathfrak{g}})$, associated to basic Lie superalgebras ${\mathfrak{g}}$ at non-admissible collapsing levels $k$, having exactly one irreducible ${\mathfrak{g}}$-locally finite module in the category ${\mathcal O}$. In the case when ${\mathfrak{g}}$ is a Lie algebra, we prove a complete reducibility result for $V_k({\mathfrak{g}})$-modules at an arbitrary collapsing level. We also determine the generators of the maximal ideal in the universal affine vertex algebra $V^k ({\mathfrak{g}})$ at certain negative integer levels. Considering some conformal embeddings in the simple affine vertex algebras $V_{-1/2} (C_n)$ and $V_{-4}(E_7)$, we surprisingly obtain the realization of non-simple affine vertex algebras of types $B$ and $D$ having exactly one nontrivial ideal.

Sign in / Sign up

Export Citation Format

Share Document