scholarly journals The massive supermembrane on a knot

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
M. P. Garcia del Moral ◽  
P. Leon ◽  
A. Restuccia
Keyword(s):  
Critical Points ◽  
Hamiltonian Formulation ◽  
Cosmological Term ◽  
Target Space ◽  
Finite Multiplicity ◽  
Torus Bundle ◽  
Minkowski Space Time ◽  
Punctured Torus ◽  
Mass Terms ◽  
The One

Abstract We obtain the Hamiltonian formulation of the 11D Supermembrane theory non-trivially compactified on a twice punctured torus times a 9D Minkowski space-time. It corresponds to a M2-brane formulated in 11D space with ten non-compact dimensions. The critical points like the poles and the zeros of the fields describing the embedding of the Supermembrane in the target space are treated rigorously. The non-trivial compactification generates non-trivial mass terms appearing in the bosonic potential, which dominate the full supersymmetric potential and should render the spectrum of the (regularized) Supermembrane discrete with finite multiplicity. The behaviour of the fields around the punctures generates a cosmological term in the Hamiltonian of the theory.The massive supermembrane can also be seen as a nontrivial uplift of a supermembrane torus bundle with parabolic monodromy in M9 × T2. The moduli of the theory is the one associated with the punctured torus, hence it keeps all the nontriviality of the torus moduli even after the decompactification process to ten noncompact dimensions. The formulation of the theory on a punctured torus bundle is characterized by the (1, 1) − knots associated with the monodromies.

scholarly journals Fluxes, twisted tori, monodromy and U(1) supermembranes

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
M. P. Garcia del Moral ◽  
C. Las Heras ◽  
P. Leon ◽  
J. M. Pena ◽  
A. Restuccia
Keyword(s):  
Geometrical Structure ◽  
Central Charge ◽  
Target Space ◽  
Finite Multiplicity ◽  
Torus Bundle ◽  
Zero Modes ◽  
World Volume ◽  
The World ◽  
Area Preserving ◽  
Brane Theory

Abstract We show that the D = 11 supermembrane theory (M2-brane) compactified on a M9× T2 target space, with constant fluxes C± naturally incorporates the geometrical structure of a twisted torus. We extend the M2-brane theory to a formulation on a twisted torus bundle. It is consistently fibered over the world volume of the M2-brane. It can also be interpreted as a torus bundle with a nontrivial U(1) connection associated to the fluxes. The structure group G is the area preserving diffeomorphisms. The torus bundle is defined in terms of the monodromy associated to the isotopy classes of symplectomorphisms with π0(G) = SL(2, Z), and classified by the coinvariants of the subgroups of SL(2, Z). The spectrum of the theory is purely discrete since the constant flux induces a central charge on the supersymmetric algebra and a modification on the Hamiltonian which renders the spectrum discrete with finite multiplicity. The theory is invariant under symplectomorphisms connected and non connected to the identity, a result relevant to guarantee the U-dual invariance of the theory. The Hamiltonian of the theory exhibits interesting new U(1) gauge and global symmetries on the worldvolume induced by the symplectomorphim transformations. We construct explicitly the supersymmetric algebra with nontrivial central charges. We show that the zero modes decouple from the nonzero ones. The nonzero mode algebra corresponds to a massive superalgebra that preserves either 1/2 or 1/4 of the original supersymmetry depending on the state considered.

scholarly journals HETEROTIC T-DUALITY AND THE RENORMALIZATION GROUP

1999 ◽  
Vol 14 (14) ◽  
pp. 2257-2271 ◽  
Author(s):  
KASPER OLSEN ◽  
RICARDO SCHIAPPA
Keyword(s):  
Renormalization Group ◽  
Sigma Models ◽  
Sigma Model ◽  
Beta Function ◽  
Target Space ◽  
Loop Order ◽  
Duality Transformations ◽  
Duality Symmetry ◽  
The One ◽  
Renormalization Group Flows

We consider target space duality transformations for heterotic sigma models and strings away from renormalization group fixed points. By imposing certain consistency requirements between the T-duality symmetry and renormalization group flows, the one-loop gauge beta function is uniquely determined, without any diagram calculations. Classical T-duality symmetry is a valid quantum symmetry of the heterotic sigma model, severely constraining its renormalization flows at this one-loop order. The issue of heterotic anomalies and their cancellation is addressed from this duality constraining viewpoint.

FIVEBRANE STRUCTURES

2009 ◽  
Vol 21 (10) ◽  
pp. 1197-1240 ◽  
Author(s):  
HISHAM SATI ◽  
URS SCHREIBER ◽  
JIM STASHEFF
Keyword(s):  
String Theory ◽  
Heterotic String ◽  
Target Space ◽  
Type Ii ◽  
Anomaly Cancellation ◽  
Heterotic String Theory ◽  
Dual Version ◽  
String Structure ◽  
Topological Obstructions ◽  
The One

We study the cohomological physics of fivebranes in type II and heterotic string theory. We give an interpretation of the one-loop term in type IIA, which involves the first and second Pontrjagin classes of spacetime, in terms of obstructions to having bundles with certain structure groups. Using a generalization of the Green–Schwarz anomaly cancellation in heterotic string theory which demands the target space to have a String structure, we observe that the "magnetic dual" version of the anomaly cancellation condition can be read as a higher analog of String structure, which we call Fivebrane structure. This involves lifts of orthogonal and unitary structures through higher connected covers which are not just 3- but even 7-connected. We discuss the topological obstructions to the existence of Fivebrane structures. The dual version of the anomaly cancellation points to a relation of string and Fivebrane structures under electric-magnetic duality.

Weak interactions in chain polymers [M(μ-X)2 L 2]∞ (M = Zn, Cd; X = Cl, Br; L = substituted pyridine) – an electron density study

2009 ◽  
Vol 65 (5) ◽  
pp. 600-611 ◽  
Author(s):  
Ruimin Wang ◽  
Christian W. Lehmann ◽  
Ulli Englert
Keyword(s):  
Hydrogen Bonds ◽  
Electron Density ◽  
Critical Points ◽  
Weak Interactions ◽  
Data Sets ◽  
X Ray Diffraction ◽  
Density Distributions ◽  
The One ◽  
Experimental Electron Density ◽  
Density Study

The experimental electron-density distributions in crystals of five chain polymers [M(μ-X)2(py)2] (M = Zn, Cd; X = Cl, Br; py = 3,5-substituted pyridine) have been obtained from high-resolution X-ray diffraction data sets (sin θ/λ > 1.1 Å−1) at 100 K. Topological analyses following Bader's `Atoms in Molecules' approach not only confirmed the existence of (3, −1) critical points for the chemically reasonable and presumably strong covalent and coordinative bonds, but also for four different secondary interactions which are expected to play a role in stabilizing the polymeric structures which are unusual for Zn as the metal center. These weaker contacts comprise intra- and inter-strand C—H...X—M hydrogen bonds on the one hand and C—X...X—C interhalogen contacts on the other hand. According to the experimental electron-density studies, the non-classical hydrogen bonds are associated with higher electron density in the (3, −1) critical points than the halogen bonds and hence are the dominant interactions both with respect to intra- and inter-chain contacts.

scholarly journals GENERAL RELATIVITY AS A THEORY OF TWO CONNECTIONS

1994 ◽  
Vol 03 (02) ◽  
pp. 379-392 ◽  
Author(s):  
J. FERNANDO BARBERO G.
Keyword(s):  
General Relativity ◽  
Phase Space ◽  
Hamiltonian Formulation ◽  
The One

We show in this paper that it is possible to formulate general relativity in a phase space coordinatized by two SO(3) connections. We analyze first the Husain-Kuchař model and find a two connection description for it. Introducing a suitable scalar constraint in this phase space we get a Hamiltonian formulation of gravity that is close to the one given by Ashtekar, from which it is derived, but has some interesting features of its own. Among them are a possible mechanism for dealing with the degenerate metrics and a neat way of writing the constraints of general relativity.

scholarly journals Cluster Luttinger liquids and emergent supersymmetric conformal critical points in the one-dimensional soft-shoulder Hubbard model

2015 ◽  
Vol 92 (4) ◽  
Author(s):  
M. Dalmonte ◽  
W. Lechner ◽  
Zi Cai ◽  
M. Mattioli ◽  
A. M. Läuchli ◽  
...  
Keyword(s):  
Hubbard Model ◽  
Critical Points ◽  
Luttinger Liquids ◽  
One Dimensional ◽  
The One

ZETA-FUNCTION REGULARIZATION APPROACH TO FINITE TEMPERATURE EFFECTS IN KALUZA-KLEIN SPACE-TIMES

1992 ◽  
Vol 07 (29) ◽  
pp. 2669-2683 ◽  
Author(s):  
ANDREI A. BYTSENKO ◽  
LUCIANO VANZO ◽  
SERGIO ZERBINI
Keyword(s):  
Zeta Function ◽  
Finite Temperature ◽  
Space Time ◽  
Discrete Torsion ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space ◽  
High Temperature Expansion ◽  
Kernel Approach ◽  
The One ◽  
Kaluza Klein

In the framework of heat-kernel approach to zeta-function regularization, the one-loop effective potential at finite temperature for scalar and spinor fields on Kaluza-Klein space-time of the form [Formula: see text], where MP is p-dimensional Minkowski space-time is evaluated. In particular, when the compact manifold is [Formula: see text], the Selberg trace formula associated with discrete torsion-free group Γ of the n-dimensional Lobachevsky space Hn is used. An explicit representation for the thermodynamic potential valid for arbitrary temperature is found. As a result a complete high temperature expansion is presented and the roles of zero modes and topological contributions is discussed.

scholarly journals Fermion mass hierarchy in grand gauge-Higgs unification

2019 ◽  
Vol 2019 (8) ◽  
Author(s):  
Nobuhito Maru ◽  
Yoshiki Yatagai
Keyword(s):  
Top Quark ◽  
Electroweak Symmetry Breaking ◽  
Boson Mass ◽  
Fermion Mass ◽  
Mass Hierarchy ◽  
Electroweak Symmetry ◽  
Fermion Masses ◽  
The Standard Model ◽  
Mass Terms ◽  
The One

Abstract Grand gauge-Higgs unification of 5D $SU(6)$ gauge theory on an orbifold $S^1/Z_2$ is discussed. The Standard Model (SM) fermions are introduced on one of the boundaries and some massive bulk fields are also introduced so that they couple to the SM fermions through the mass terms on the boundary. Integrating out the bulk fields generates SM fermion masses with exponentially small bulk mass dependences. The SM fermion masses except for the top quark are shown to be reproduced by mild tuning of the bulk masses. The one-loop Higgs potential is calculated and it is shown that electroweak symmetry breaking occurs by introducing additional bulk fields. The Higgs boson mass is also computed.

FOUR-DIMENSIONAL TWO-BRANE SOLUTION IN CHIRAL GAUGED WESS-ZUMINO-WITTEN MODEL

1992 ◽  
Vol 07 (32) ◽  
pp. 2999-3006 ◽  
Author(s):  
SWAPNA MAHAPATRA
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Target Space ◽  
Curvature Singularity ◽  
One Dimensional ◽  
Conformal Field ◽  
Witten Theory ◽  
Brane Solution ◽  
The One ◽  
String Propagation

An exact conformal field theory describing a four-dimensional two-brane solution is found by considering a chiral gauged Wess-Zumino-Witten theory corresponding to SL (2, R)× R, where one gauges the one-dimensional U(1) subgroup together with a translation in R. The backgrounds for string propagation are explicitly obtained and the target space is shown to have a true curvature singularity.

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