scholarly journals Perturbative F-theory 10-brane and M-theory 5-brane

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Machiko Hatsuda ◽  
Warren Siegel
Keyword(s):  
Current Algebra ◽  
Duality Theory ◽  
Virasoro Algebra ◽  
Space Time ◽  
Lagrangian Formulation ◽  
Gauge Fields ◽  
Duality Symmetry ◽  
M Theory ◽  
Current Algebras

Abstract The exceptional symmetry is realized perturbatively in F-theory which is the manifest U-duality theory. The SO(5) U-duality symmetry acts on both the 16 space-time coordinates and the 10 worldvolume coordinates. Closure of the Virasoro algebra requires the Gauss law constraints on the worldvolume. This set of current algebras describes a F-theory 10-brane. The SO(5) duality symmetry is enlarged to the SO(6) symmetry in the Lagrangian formulation. We propose actions of the F-theory 10-brane with SO(5) and SO(6) symmetries. The gauge fields of the latter action are coset elements of SO(6)/SO(6; ℂ) which include both the SO(5)/SO(5; ℂ) spacetime backgrounds and the worldvolume backgrounds. The SO(5) current algebra obtained from the Pasti-Sorokin-Tonin M5-brane Lagrangian leads to the theory behind M-theory, namely F-theory. We also propose an action of the perturbative M-theory 5-brane obtained by sectioning the worldvolume of the F-theory 10-brane.

scholarly journals Brane current algebras and generalised geometry from QP manifolds. Or, “when they go high, we go low”

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Alex S. Arvanitakis
Keyword(s):  
Current Algebra ◽  
Poisson Algebra ◽  
Gauge Fields ◽  
Complex Structures ◽  
Poisson Brackets ◽  
Geometric Form ◽  
Free Current ◽  
Universal Expression ◽  
Current Algebras

Abstract We construct a Poisson algebra of brane currents from a QP-manifold, and show their Poisson brackets take a universal geometric form. This generalises a result of Alekseev and Strobl on string currents and generalised geometry to include branes with worldvolume gauge fields, such as the D3 and M5. Our result yields a universal expression for the ’t Hooft anomaly that afflicts isometries in the presence of fluxes. We determine the current algebra in terms of (exceptional) generalised geometry, and show that the tensor hierarchy gives rise to a brane current hierarchy. Exceptional complex structures produce pairs of anomaly-free current subalgebras on the M5-brane worldvolume.

scholarly journals Currents, charges and algebras in exceptional generalised geometry

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
David Osten
Keyword(s):  
Current Algebra ◽  
Hamiltonian Formulation ◽  
Building Blocks ◽  
Lie Derivative ◽  
Consistency Check ◽  
World Volume ◽  
Invariant Currents ◽  
Invariant Current ◽  
M Theory ◽  
A Current

Abstract A classical Ed(d)-invariant Hamiltonian formulation of world-volume theories of half-BPS p-branes in type IIb and eleven-dimensional supergravity is proposed, extending known results to d ≤ 6. It consists of a Hamiltonian, characterised by a generalised metric, and a current algebra constructed s.t. it reproduces the Ed(d) generalised Lie derivative. Ed(d)-covariance necessitates the introduction of so-called charges, specifying the type of p-brane and the choice of section. For p > 2, currents of p-branes are generically non- geometric due to the imposition of U-duality, e.g. the M5-currents contain coordinates associated to the M2-momentum.A derivation of the Ed(d)-invariant current algebra from a canonical Poisson structure is in general not possible. At most, one can derive a current algebra associated to para-Hermitian exceptional geometry.The membrane in the SL(5)-theory is studied in detail. It is shown that in a generalised frame the current algebra is twisted by the generalised fluxes. As a consistency check, the double dimensional reduction from membranes in M-theory to strings in type IIa string theory is performed. Many features generalise to p-branes in SL(p + 3) generalised geometries that form building blocks for the Ed(d)-invariant currents.

MANIFOLD-SPLITTING REGULARIZATION, SELF-LINKING, TWISTING, WRITHING NUMBERS OF SPACE-TIME RIBBONS and POLYAKOV’S PROOF OF FERMI-BOSE TRANSMUTATIONS

1988 ◽  
Vol 03 (08) ◽  
pp. 1959-1979 ◽  
Author(s):  
CHIA-HSIUNG TZE
Keyword(s):  
Integral Formula ◽  
Space Time ◽  
Gauge Fields ◽  
Alternative Formulation ◽  
Complex Numbers ◽  
Closed Space ◽  
Feynman Path ◽  
Higher Dimensional ◽  
Linking Coefficient ◽  
In Memoriam

We present an alternative formulation of Polyakov’s regularization of Gauss’ integral formula for a single closed Feynman path. A key element in his proof of the D=3 fermi-bose transmutations induced by topological gauge fields, this regularization is linked here with the existence and properties of a nontrivial topological invariant for a closed space ribbon. This self-linking coefficient, an integer, is the sum of two differential characteristics of the ribbon, its twisting and writhing numbers. These invariants form the basis for a physical interpretation of our regularization. Their connection to Polyakov’s spinorization is discussed. We further generalize our construction to the self-linking, twisting and writhing of higher dimensional d=n (odd) submanifolds in D=(2n+1) space-time. Our comprehensive analysis intends to supplement Polyakov’s work as it identifies a natural path to its higher dimensional mathematical and physical generalizations. Combining the theorems of White on self-linking of manifolds and of Adams on nontrivial Hopf fibre bundles and the four composition-division algebras, we argue that besides Polyakov’s case where (d, D)=(1, 3) tied to complex numbers, the potentially interesting extensions are two chiral models with (d, D)=(3, 7) and (7, 15) uniquely linked to quaternions and octonions. In Memoriam Richard P. Feynman

scholarly journals Lost chapters in CHL black holes: untwisted quarter-BPS dyons in the ℤ2 model

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Fabian Fischbach ◽  
Albrecht Klemm ◽  
Christoph Nega
Keyword(s):  
String Duality ◽  
Modular Forms ◽  
Black Hole Entropy ◽  
Siegel Modular Forms ◽  
Partition Functions ◽  
Twisted Sector ◽  
Duality Symmetry ◽  
Iwahori Subgroup ◽  
M Theory ◽  
Bonnet Term

Abstract Motivated by recent advances in Donaldson-Thomas theory, four-dimensional $$ \mathcal{N} $$ N = 4 string-string duality is examined in a reduced rank theory on a less studied BPS sector. In particular we identify candidate partition functions of “untwisted” quarter-BPS dyons in the heterotic ℤ2 CHL model by studying the associated chiral genus two partition function, based on the M-theory lift of string webs argument by Dabholkar and Gaiotto. This yields meromorphic Siegel modular forms for the Iwahori subgroup B(2) ⊂ Sp4(ℤ) which generate BPS indices for dyons with untwisted sector electric charge, in contrast to twisted sector dyons counted by a multiplicative lift of twisted-twining elliptic genera known from Mathieu moonshine. The new partition functions are shown to satisfy the expected constraints coming from wall-crossing and S-duality symmetry as well as the black hole entropy based on the Gauss-Bonnet term in the effective action. In these aspects our analysis confirms and extends work of Banerjee, Sen and Srivastava, which only addressed a subset of the untwisted sector dyons considered here. Our results are also compared with recently conjectured formulae of Bryan and Oberdieck for the partition functions of primitive DT invariants of the CHL orbifold X = (K3 × T2)/ℤ2, as suggested by string duality with type IIA theory on X.

scholarly journals EXTENSION OF THE POINCARÉ GROUP AND NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (31) ◽  
pp. 5765-5785 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Group ◽  
Gauge Transformation ◽  
Space Time ◽  
Gauge Fields ◽  
Poincaré Group ◽  
Matrix Representations ◽  
Poincare Group ◽  
Yang Mills ◽  
The Matrix ◽  
Transversal Plane

In the recently proposed generalization of the Yang–Mills theory, the group of gauge transformation gets essentially enlarged. This enlargement involves a mixture of the internal and space–time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space–time indices. The matrix representations of the extended Poincaré generators are expressible in terms of Pauli–Lubanski vector in one case and in terms of its invariant derivative in another. In the later case the generators of the gauge group are transversal to the momentum and are projecting the non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite spacelike components.

scholarly journals Astronomical Significance of the 137.035 999 Part of the Inverse Fine-Structure Constant

2020 ◽  
Vol 12 (2) ◽  
pp. 42
Author(s):  
Mels Sluyser
Keyword(s):  
Fine Structure ◽  
Structure Constant ◽  
Space Time ◽  
Fine Structure Constant ◽  
M Theory ◽  
Triplet Code

The inverse fine-structure constant 1/α= 137.035 satisfies 1/α = 112 + 42 + 0.035 = 121 + 16 + 0.035 = 137.035, with 11 being the 11 dimensions of M-theory, 4 the number of dimensions of Einstein’s space-time, and 0.035 the 3.5 percent visible Universe. Cosmological information appears to be encrypted linearly as a triplet code in 1/α.

THE DISLOCATION TREATMENT OF GAUGE FIELDS OF SPACE-TIME TRANSLATIONS

1987 ◽  
Vol 02 (08) ◽  
pp. 609-616 ◽  
Author(s):  
G. SARDANASHVILY ◽  
M. GOGBERSHVILY
Keyword(s):  
Dislocation Structure ◽  
Space Time ◽  
Gauge Fields

A particular "dislocation" structure of a space-time due to Poincaré translation gauge fields which results in modifications of standard gravitation effects is predicted.

scholarly journals M-THEORY DUALITY AND BPS-EXTENDED SUPERGRAVITY

2001 ◽  
Vol 16 (05) ◽  
pp. 1002-1011 ◽  
Author(s):  
BERNARD DE WIT
Keyword(s):  
Lorentz Invariance ◽  
Space Time ◽  
Duality Group ◽  
Toroidal Compactifications ◽  
Maximal Supergravity ◽  
Bps States ◽  
M Theory

We discuss toroidal compactifications of maximal supergravity coupled to an extended configuration of BPS states which transform consistently under the U-duality group. Under certain conditions this leads to theories that live in more than eleven space-time dimensions, with maximal supersymmetry but only partial Lorentz invariance. We demonstrate certain features of this construction for the case of nine-dimensional N=2 supergravity.

scholarly journals THE INTERFACE OF COSMOLOGY WITH STRING AND M(ILLENNIUM) THEORY

2001 ◽  
Vol 16 (30) ◽  
pp. 4803-4843 ◽  
Author(s):  
DAMIEN A. EASSON
Keyword(s):  
Early Universe ◽  
Extra Dimensions ◽  
Large Extra Dimensions ◽  
Short Review ◽  
Big Bang ◽  
Space Time ◽  
String Cosmology ◽  
Brane World ◽  
Recent Developments ◽  
M Theory

The purpose of this review is to discuss recent developments occurring at the interface of cosmology with string and M theory. We begin with a short review of 1980s string cosmology and the Brandenberger–Vafa mechanism for explaining space–time dimensionality. It is shown how this scenario has been modified to include the effects of p-brane gases in the early universe. We then introduce the Pre-Big-Bang scenario (PBB), Hořava–Witten heterotic M theory and the work of Lukas, Ovrut and Waldram, and end with a discussion of large extra dimensions, the Randall–Sundrum model and Brane World cosmologies.

scholarly journals Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles

2018 ◽  
Vol 175 ◽  
pp. 11007 ◽  
Author(s):  
Christof Gattringer ◽  
Daniel Göschl ◽  
Carlotta Marchis
Keyword(s):  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Space Time ◽  
Field Theories ◽  
Gauge Fields ◽  
Chiral Model ◽  
Staggered Fermions ◽  
Lattice Field ◽  
Principal Chiral Model ◽  
Matter Fields

We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes), or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles). Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure) generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2) principal chiral model with chemical potential coupled to two of the Noether charges, SU(2) lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.

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