scholarly journals T 3-invariant heterotic Hull-Strominger solutions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bobby Samir Acharya ◽  
Alex Kinsella ◽  
Eirik Eik Svanes
Keyword(s):  
Bianchi Identity ◽  
Heterotic String ◽  
Back Reaction ◽  
Flat Connection ◽  
Closure Condition ◽  
Yang Mills ◽  
Close Analogy ◽  
Local Solutions ◽  
Calabi Yau Manifolds

Abstract We consider the heterotic string on Calabi-Yau manifolds admitting a Strominger-Yau-Zaslow fibration. Upon reducing the system in the T3-directions, the Hermitian Yang-Mills conditions can then be reinterpreted as a complex flat connection on ℝ3 satisfying a certain co-closure condition. We give a number of abelian and non-abelian examples, and also compute the back-reaction on the geometry through the non-trivial α′-corrected heterotic Bianchi identity, which includes an important correction to the equations for the complex flat connection. These are all new local solutions to the Hull-Strominger system on T3× ℝ3. We also propose a method for computing the spectrum of certain non-abelian models, in close analogy with the Morse-Witten complex of the abelian models.

scholarly journals STANDARD MODEL BUNDLES OF THE HETEROTIC STRING

2006 ◽  
Vol 21 (06) ◽  
pp. 1261-1281 ◽  
Author(s):  
GOTTFRIED CURIO
Keyword(s):  
Standard Model ◽  
Spectral Data ◽  
Gauge Group ◽  
Matter Content ◽  
Heterotic String ◽  
Spectral Cover ◽  
The Standard Model ◽  
Free Involution ◽  
Simply Connected ◽  
Calabi Yau Manifolds

We show how to construct supersymmetric three-generation models with gauge group and matter content of the Standard Model in the framework of non-simply-connected elliptically fibered Calabi–Yau manifolds Z. The elliptic fibration on a cover Calabi–Yau, where the model has six generations of SU(5) and the bundle is given via the spectral cover description, has a second section leading to the needed free involution. The relevant involution on the defining spectral data of the bundle is identified for a general Calabi–Yau of this type and invariant bundles are generally constructible.

A formula for the local solution of the self-dual Yang-Mills equations

1987 ◽  
Vol 414 (1846) ◽  
pp. 135-147 ◽  
Keyword(s):  
Holomorphic Vector Bundle ◽  
Transition Function ◽  
Local Solution ◽  
The Self ◽  
Exponential Integral ◽  
Yang Mills ◽  
The Matrix ◽  
Local Solutions ◽  
Integral Analogue ◽  
Infinite Sum

Twistor techniques are used to give all local solutions to the self-dual Yang-Mills equations for any matrix gauge group. The field is expressed in terms of an infinite sum, which is a contour integral analogue of a path-ordered exponential integral, over the twistor datum. The key step is the solution of the matrix-valued Cousin-Hilbert-Riemann problem on the sphere, that is, of trivializing a holomorphic vector bundle given by a transition function over an annulus.

scholarly journals Seven-dimensional octonionic Yang-Mills instanton and its extension to an heterotic string soliton

1995 ◽  
Vol 351 (1-3) ◽  
pp. 169-172 ◽  
Author(s):  
Murat Günaydin ◽  
Hermann Nicolai
Keyword(s):  
Heterotic String ◽  
Yang Mills

scholarly journals Hermitian–Yang–Mills Connections on Collapsing Elliptically Fibered K3 Surfaces

2022 ◽  
Vol 32 (2) ◽  
Author(s):  
Ved Datar ◽  
Adam Jacob
Keyword(s):  
K3 Surfaces ◽  
Flat Connection ◽  
Generic Fiber ◽  
Yang Mills ◽  
Ricci Flat

AbstractLet $$X\rightarrow {{\mathbb {P}}}^1$$ X → P 1 be an elliptically fibered K3 surface, admitting a sequence $$\omega _{i}$$ ω i of Ricci-flat metrics collapsing the fibers. Let V be a holomorphic SU(n) bundle over X, stable with respect to $$\omega _i$$ ω i . Given the corresponding sequence $$\Xi _i$$ Ξ i of Hermitian–Yang–Mills connections on V, we prove that, if E is a generic fiber, the restricted sequence $$\Xi _i|_{E}$$ Ξ i | E converges to a flat connection $$A_0$$ A 0 . Furthermore, if the restriction $$V|_E$$ V | E is of the form $$\oplus _{j=1}^n{\mathcal {O}}_E(q_j-0)$$ ⊕ j = 1 n O E ( q j - 0 ) for n distinct points $$q_j\in E$$ q j ∈ E , then these points uniquely determine $$A_0$$ A 0 .

Heterotic string modifications of Einstein's and Yang-Mills' actions

1986 ◽  
Vol 176 (1-2) ◽  
pp. 57-60 ◽  
Author(s):  
Y. Kikuchi ◽  
C. Marzban ◽  
Y.J. Ng
Keyword(s):  
Heterotic String ◽  
Yang Mills

scholarly journals Supersymmetry, T-duality and heterotic α′-corrections

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Eric Lescano ◽  
Carmen A. Núñez ◽  
Jesús A. Rodríguez
Keyword(s):  
Effective Field ◽  
Heterotic String ◽  
Supersymmetry Algebra ◽  
Yang Mills ◽  
First Order ◽  
Duality Symmetry ◽  
Transformation Rules ◽  
Higher Derivative ◽  
String Spectrum ◽  
Fermionic Fields

Abstract Higher-derivative interactions and transformation rules of the fields in the effective field theories of the massless string states are strongly constrained by space-time symmetries and dualities. Here we use an exact formulation of ten dimensional $$ \mathcal{N} $$ N = 1 supergravity coupled to Yang-Mills with manifest T-duality symmetry to construct the first order α′-corrections of the heterotic string effective action. The theory contains a supersymmetric and T-duality covariant generalization of the Green-Schwarz mechanism that determines the modifications to the leading order supersymmetry transformation rules of the fields. We compute the resulting field-dependent deformations of the coefficients in the supersymmetry algebra and construct the invariant action, with up to and including four-derivative terms of all the massless bosonic and fermionic fields of the heterotic string spectrum.

scholarly journals (MS)SM-like models on smooth Calabi-Yau manifolds from all three heterotic string theories

2015 ◽  
Vol 63 (9-10) ◽  
pp. 609-632 ◽  
Author(s):  
Stefan Groot Nibbelink ◽  
Orestis Loukas ◽  
Fabian Ruehle
Keyword(s):  
Heterotic String ◽  
Heterotic String Theories ◽  
String Theories ◽  
Calabi Yau Manifolds

scholarly journals Optimal Łojasiewicz–Simon inequalities and Morse–Bott Yang–Mills energy functions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Paul M. N. Feehan
Keyword(s):  
Energy Function ◽  
Regular Point ◽  
Direct Analysis ◽  
Flat Connection ◽  
Energy Functions ◽  
Yang Mills ◽  
Small Curvature ◽  
Banach Manifolds ◽  
Hessian Operator ◽  
Four Manifolds

Abstract For any compact Lie group 𝐺 and closed, smooth Riemannian manifold ( X , g ) (X,g) of dimension d ≥ 2 d\geq 2 , we extend a result due to Uhlenbeck (1985) that gives existence of a flat connection on a principal 𝐺-bundle over 𝑋 supporting a connection with L p L^{p} -small curvature, when p > d / 2 p>d/2 , to the case of a connection with L d / 2 L^{d/2} -small curvature. We prove an optimal Łojasiewicz–Simon gradient inequality for abstract Morse–Bott functions on Banach manifolds, generalizing an earlier result due to the author and Maridakis (2019), principally by removing the hypothesis that the Hessian operator be Fredholm with index zero. We apply this result to prove the optimal Łojasiewicz–Simon gradient inequality for the self-dual Yang–Mills energy function near regular anti-self-dual connections over closed Riemannian four-manifolds and for the full Yang–Mills energy function over closed Riemannian manifolds of dimension d ≥ 2 d\geq 2 , when known to be Morse–Bott at a given Yang–Mills connection. We also prove the optimal Łojasiewicz–Simon gradient inequality by direct analysis near a given flat connection that is a regular point of the curvature map.

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