U-duality and M-theory, an algebraic approach

The Lie-algebraic approach has been applied to solve the bond pricing problem in single-factor interest rate models. Four of the popular single-factor models, namely, the Vasicek model, Cox-Ingersoll-Ross model, double square-root model, and Ahn-Gao model, are investigated. By exploiting the dynamical symmetry of their bond pricing equations, analytical closed-form pricing formulae can be derived in a straightfoward manner. Time-varying model parameters could also be incorporated into the derivation of the bond price formulae, and this has the added advantage of allowing yield curves to be fitted. Furthermore, the Lie-algebraic approach can be easily extended to formulate new analytically tractable single-factor interest rate models.

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Currents, charges and algebras in exceptional generalised geometry

Journal of High Energy Physics ◽

10.1007/jhep06(2021)070 ◽

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.

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Explicit soft supersymmetry breaking in the heterotic M-theory B − L MSSM

Journal of High Energy Physics ◽

10.1007/jhep08(2021)033 ◽

2021 ◽

Vol 2021 (8) ◽

Author(s):

Anthony Ashmore ◽

Sebastian Dumitru ◽

Burt A. Ovrut

Keyword(s):

Line Bundle ◽

Supersymmetry Breaking ◽

Moduli Space ◽

Initial Conditions ◽

Low Energy ◽

Strongly Coupled ◽

Hidden Sector ◽

Effective Lagrangian ◽

Soft Supersymmetry Breaking ◽

M Theory

Abstract The strongly coupled heterotic M-theory vacuum for both the observable and hidden sectors of the B − L MSSM theory is reviewed, including a discussion of the “bundle” constraints that both the observable sector SU(4) vector bundle and the hidden sector bundle induced from a single line bundle must satisfy. Gaugino condensation is then introduced within this context, and the hidden sector bundles that exhibit gaugino condensation are presented. The condensation scale is computed, singling out one line bundle whose associated condensation scale is low enough to be compatible with the energy scales available at the LHC. The corresponding region of Kähler moduli space where all bundle constraints are satisfied is presented. The generic form of the moduli dependent F-terms due to a gaugino superpotential — which spontaneously break N = 1 supersymmetry in this sector — is presented and then given explicitly for the unique line bundle associated with the low condensation scale. The moduli-dependent coefficients for each of the gaugino and scalar field soft supersymmetry breaking terms are computed leading to a low-energy effective Lagrangian for the observable sector matter fields. We then show that at a large number of points in Kähler moduli space that satisfy all “bundle” constraints, these coefficients are initial conditions for the renormalization group equations which, at low energy, lead to completely realistic physics satisfying all phenomenological constraints. Finally, we show that a substantial number of these initial points also satisfy a final constraint arising from the quadratic Higgs-Higgs conjugate soft supersymmetry breaking term.

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Singular BPS boundary conditions in $$ \mathcal{N} $$ = (2, 2) supersymmetric gauge theories

Journal of High Energy Physics ◽

10.1007/jhep03(2021)043 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Tadashi Okazaki ◽

Douglas J. Smith

Keyword(s):

String Theory ◽

Boundary Conditions ◽

Gauge Theories ◽

Holomorphic Curve ◽

Two Dimensional ◽

Supersymmetric Gauge Theories ◽

Special Lagrangian ◽

Supersymmetric Gauge ◽

M Theory

Abstract We derive general BPS boundary conditions in two-dimensional $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow the bulk fields to have poles at the boundary. We also present the brane configurations for the half- and quarter-BPS boundary conditions of the $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories in terms of branes in Type IIA string theory. We find that both A-type and B-type brane configurations are lifted to M-theory as a system of M2-branes ending on an M5-brane wrapped on a product of a holomorphic curve in ℂ2 with a special Lagrangian 3-cycle in ℂ3.

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The “Emerging” Reality from “Hidden” Spaces

Universe ◽

10.3390/universe7030075 ◽

2021 ◽

Vol 7 (3) ◽

pp. 75

Author(s):

Richard Pincak ◽

Alexander Pigazzini ◽

Saeid Jafari ◽

Cenap Ozel

Keyword(s):

Dark Matter ◽

String Theory ◽

Topological Approach ◽

New Approach ◽

Topological Interpretation ◽

New Interpretation ◽

M Theory

The main purpose of this paper is to show and introduce some new interpretative aspects of the concept of “emergent space” as geometric/topological approach in the cosmological field. We will present some possible applications of this theory, among which the possibility of considering a non-orientable wormhole, but mainly we provide a topological interpretation, using this new approach, to M-Theory and String Theory in 10 dimensions. Further, we present some conclusions which this new interpretation suggests, and also some remarks considering a unifying approach between strings and dark matter. The approach shown in the paper considers that reality, as it appears to us, can be the “emerging” part of a more complex hidden structure. Pacs numbers: 11.25.Yb; 11.25.-w; 02.40.Ky; 02.40.-k; 04.50.-h; 95.35.+d.

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