Exceptional field theory. I.E6(6)-covariant form of M-theory and type IIB

Abstract We study circle compactifications of 6d superconformal field theories giving rise to 5d rank 1 and rank 2 Kaluza-Klein theories. We realise the resulting theories as M-theory compactifications on local Calabi-Yau 3-folds and match the prepotentials from geometry and field theory. One novelty in our approach is that we include explicit dependence on bare gauge couplings and mass parameters in the description which in turn leads to an accurate parametrisation of the prepotential including all parameters of the field theory. We find that the resulting geometries admit “fibre-base” duality which relates their six-dimensional origin with the purely five-dimensional quantum field theory interpretation. The fibre-base duality is realised simply by swapping base and fibre curves of compact surfaces in the local Calabi-Yau which can be viewed as the total space of the anti-canonical bundle over such surfaces. Our results show that such swappings precisely occur for surfaces with a zero self-intersection of the base curve and result in an exchange of the 6d and 5d pictures.

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The classical double copy for M-theory from a Kerr-Schild ansatz for exceptional field theory

Journal of High Energy Physics ◽

10.1007/jhep04(2021)071 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

David S. Berman ◽

Kwangeon Kim ◽

Kanghoon Lee

Keyword(s):

Field Theory ◽

State Of The Art ◽

Single Copy ◽

Current State ◽

M Theory ◽

Double Copy

Abstract We construct the classical double copy formalism for M-theory. This extends the current state of the art by including the three form potential of eleven dimensional supergravity along with the metric. The key for this extension is to construct a Kerr-Schild type Ansatz for exceptional field theory. This Kerr-Schild Ansatz then allows us to find the solutions of charged objects such as the membrane from a set of single copy fields. The exceptional field theory formalism then automatically produces the IIB Kerr-Schild ansatz allowing the construction of the single copy for the fields of IIB supergravity (with manifest SL(2) symmetry).

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SUPERGRAVITY DESCRIPTION OF FIELD THEORIES ON CURVED MANIFOLDS AND A NO GO THEOREM

International Journal of Modern Physics A ◽

10.1142/s0217751x01003937 ◽

2001 ◽

Vol 16 (05) ◽

pp. 822-855 ◽

Cited By ~ 580

Author(s):

JUAN MALDACENA ◽

CARLOS NUÑEZ

Keyword(s):

Field Theory ◽

Conformal Field Theory ◽

Riemann Surface ◽

Riemann Surfaces ◽

Field Theories ◽

De Sitter ◽

Curved Manifolds ◽

Conformal Field ◽

Low Energies ◽

M Theory

In the first part of this paper we find supergravity solutions corresponding to branes on worldvolumes of the form Rd×Σ where Σ is a Riemann surface. These theories arise when we wrap branes on holomorphic Riemann surfaces inside K3 or CY manifolds. In some cases the theory at low energies is a conformal field theory with two less dimensions. We find some non-singular supersymmetric compactifications of M-theory down to AdS5. We also propose a criterion for permissible singularities in supergravity solutions. In the second part of this paper, which can be read independently of the first, we show that there are no non-singular Randall-Sundrum or de-Sitter compactifications for large class of gravity theories.

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Vacuum Constraints for Realistic Strongly Coupled Heterotic M-Theories

Symmetry ◽

10.3390/sym10120723 ◽

2018 ◽

Vol 10 (12) ◽

pp. 723

Author(s):

Burt Ovrut

Keyword(s):

Field Theory ◽

Vector Bundle ◽

Domain Wall ◽

Effective Field Theory ◽

Effective Field ◽

Anomaly Cancellation ◽

Strongly Coupled ◽

Hidden Sector ◽

M Theory ◽

Bulk Space

The compactification from the 11-dimensional Horava-Witten orbifold to 5-dimensional heterotic M-theory on a Schoen Calabi-Yau threefold is reviewed, as is the specific S U ( 4 ) vector bundle leading to the “heterotic standard model” in the observable sector. A generic formalism for a consistent hidden sector gauge bundle, within the context of strongly coupled heterotic M-theory, is presented. Anomaly cancellation and the associated bulk space 5-branes are discussed in this context. The further compactification to a 4-dimensional effective field theory on a linearized BPS double domain wall is then presented to order κ 11 4 / 3 . Specifically, the generic constraints required for anomaly cancellation and by the linearized domain wall solution, restrictions imposed by the vanishing of the D-terms and, finally, the constraints imposed by the necessity for positive, perturbative squared gauge couplings to this order are presented in detail.

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Cosmic strings and superstrings

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2009.0591 ◽

2010 ◽

Vol 466 (2115) ◽

pp. 623-657 ◽

Cited By ~ 110

Author(s):

Edmund J. Copeland ◽

T. W. B. Kibble

Keyword(s):

Field Theory ◽

String Theory ◽

Symmetry Breaking ◽

Cosmic Strings ◽

Grand Unification ◽

Brane Inflation ◽

Fundamental String ◽

History Of ◽

M Theory ◽

The Universe

Cosmic strings are predicted by many field-theory models, and may have been formed at a symmetry-breaking transition early in the history of the universe, such as that associated with grand unification. They could have important cosmological effects. Scenarios suggested by fundamental string theory or M-theory, in particular the popular idea of brane inflation, also strongly suggest the appearance of similar structures. Here we review the reasons for postulating the existence of cosmic strings or superstrings, the various possible ways in which they might be detected observationally and the special features that might discriminate between ordinary cosmic strings and superstrings.

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Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective

SciPost Physics ◽

10.21468/scipostphys.6.5.052 ◽

2019 ◽

Vol 6 (5) ◽

Cited By ~ 17

Author(s):

Cyril Closset ◽

Michele Del Zotto ◽

Vivek Saxena

Keyword(s):

Field Theory ◽

Gauge Theory ◽

Gauge Theories ◽

Low Energy ◽

Field Theories ◽

Isolated Singularity ◽

Coulomb Branch ◽

Superconformal Field Theories ◽

Ale Space ◽

M Theory

We revisit the correspondence between Calabi-Yau (CY) threefold isolated singularities \mathbf{X}𝐗 and five-dimensional superconformal field theories (SCFTs), which arise at low energy in M-theory on the space-time transverse to \mathbf{X}𝐗. Focussing on the case of toric CY singularities, we analyze the “gauge-theory phases” of the SCFT by exploiting fiberwise M-theory/type IIA duality. In this setup, the low-energy gauge group simply arises on stacks of coincident D6-branes wrapping 2-cycles in some ALE space of type A_{M-1}AM−1 fibered over a real line, and the map between the Kähler parameters of \mathbf{X}𝐗 and the Coulomb branch parameters of the field theory (masses and VEVs) can be read off systematically. Different type IIA “reductions” give rise to different gauge theory phases, whose existence depends on the particular (partial) resolutions of the isolated singularity \mathbf{X}𝐗. We also comment on the case of non-isolated toric singularities. Incidentally, we propose a slightly modified expression for the Coulomb-branch prepotential of 5d \mathcal{N}=1𝒩=1 gauge theories.

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M theory as a holographic field theory

Physical Review D ◽

10.1103/physrevd.59.046004 ◽

1999 ◽

Vol 59 (4) ◽

Cited By ~ 67

Author(s):

Petr Hořava

Keyword(s):

Field Theory ◽

M Theory

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TOWARDS SO(2, 10)-INVARIANT M-THEORY: MULTI-LAGRANGIAN FIELDS

Modern Physics Letters A ◽

10.1142/s0217732300000736 ◽

2000 ◽

Vol 15 (11n12) ◽

pp. 747-759 ◽

Cited By ~ 8

Author(s):

R. MANVELYAN ◽

R. MKRTCHYAN

Keyword(s):

Field Theory ◽

Equation Of Motion ◽

Space Time ◽

Unitary Representations ◽

Rank Tensor ◽

M Theory ◽

Bosonic Part

The SO (2, 10) covariant extension of M-theory superalgebra is considered, with the aim to construct a correspondingly generalized M-theory, or 11-D supergravity. For the orbit corresponding to the 11-D supergravity multiplet, the simplest unitary representations of the bosonic part of this algebra, with sixth-rank tensor excluded, are constructed on a language of field theory in 66-D space–time. The main peculiarities are the presence of more than one equation of motion and the corresponding Lagrangians for a given field and that the gauge and SUSY invariances of the theory mean that the sum of variations of these Lagrangians (with different variations of the same field) is equal to zero.

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M-Theory from Worldsheet Defects in Liouville String

Modern Physics Letters A ◽

10.1142/s0217732397002946 ◽

1997 ◽

Vol 12 (36) ◽

pp. 2813-2827 ◽

Cited By ~ 4

Author(s):

John Ellis ◽

N. E. Mavromatos ◽

D. V. Nanopoulos

Keyword(s):

Field Theory ◽

Black Holes ◽

Critical Behavior ◽

Theory Model ◽

Time Dimension ◽

Natural Embedding ◽

Field Theory Model ◽

Extra Space ◽

M Theory ◽

Liouville Dynamics

We have argued previously that black holes may be represented in a D-brane approach by monopole and vortex defects in a sine–Gordon field theory model of Liouville dynamics on the worldsheet. Supersymmetrizing this sine–Gordon system, we find critical behavior in 11 dimensions, due to defect condensation which we interpret as the worldsheet analog of D-brane condensation around an extra space–time dimension in M-theory. This supersymmetric description of Liouville dynamics has a natural embedding within a 12-dimensional framework suggestive of F-theory.

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Higher-form symmetries in 5d

Journal of High Energy Physics ◽

10.1007/jhep09(2020)024 ◽

2020 ◽

Vol 2020 (9) ◽

Cited By ~ 5

Author(s):

David R. Morrison ◽

Sakura Schäfer-Nameki ◽

Brian Willett

Keyword(s):

Field Theory ◽

Wilson Line ◽

Geometric Realization ◽

Point Of View ◽

Field Theories ◽

Quantum Field Theories ◽

Quantum Field ◽

Geometric Criterion ◽

Theory Point ◽

M Theory

Abstract We study higher-form symmetries in 5d quantum field theories, whose charged operators include extended operators such as Wilson line and ’t Hooft operators. We outline criteria for the existence of higher-form symmetries both from a field theory point of view as well as from the geometric realization in M-theory on non-compact Calabi-Yau threefolds. A geometric criterion for determining the higher-form symmetry from the intersection data of the Calabi-Yau is provided, and we test it in a multitude of examples, including toric geometries. We further check that the higher-form symmetry is consistent with dualities and is invariant under flop transitions, which relate theories with the same UV-fixed point. We explore extensions to higher-form symmetries in other compactifications of M-theory, such as G2-holonomy manifolds, which give rise to 4d $$ \mathcal{N} $$ N = 1 theories.

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