Quiver Structure of Heterotic Moduli

Seung-Joo Lee; Yang-Hui He

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Quiver Structure of Heterotic Moduli

Yang-Hui He, Seung-Joo Lee

High Energy Physics - Theory · Submitted 15 Aug 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Phenomena such as stability walls, crossing between chambers of supersymmetry, splitting of non-Abelian bundles and dynamic generation of D-terms are succinctly encoded into finite quivers.

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We analyse the vector bundle moduli arising from generic heterotic compactifications from the point of view of quiver representations. Phenomena such as stability walls, crossing between chambers of supersymmetry, splitting of non-Abelian bundles and dynamic generation of D-terms are succinctly encoded into finite quivers. By studying the Poincar\'e polynomial of the quiver moduli space using the Reineke formula, we can learn about such useful concepts as Donaldson-Thomas invariants, instanton transitions and supersymmetry breaking.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We analyse the vector bundle moduli arising from generic heterotic compactifications from the point of view of quiver representations.	contribution 0.99	0.92	0.08	asserted 0.96
s1	Phenomena such as stability walls, crossing between chambers of supersymmetry, splitting of non-Abelian bundles and dynamic generation of D-terms are succinctly encoded into finite quivers.	result 0.53	0.49	0.36	asserted 0.98
s2	By studying the Poincar\'e polynomial of the quiver moduli space using the Reineke formula, we can learn about such useful concepts as Donaldson-Thomas invariants, instanton transitions and supersymmetry breaking.	method 0.46	0.58	0.32	hedged possibility 0.66

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Original abstract

We analyse the vector bundle moduli arising from generic heterotic compactifications from the point of view of quiver representations. Phenomena such as stability walls, crossing between chambers of supersymmetry, splitting of non-Abelian bundles and dynamic generation of D-terms are succinctly encoded into finite quivers. By studying the Poincar\'e polynomial of the quiver moduli space using the Reineke formula, we can learn about such useful concepts as Donaldson-Thomas invariants, instanton transitions and supersymmetry breaking.

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1 arXiv paper cite this in 1 sentence

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Note that the adjacency matrix is computed using the information about line bundle cohomology on $X$ [ref] : l_12 = h^1(X, L_1 ⊗L_2 ^ *) = h^1(X, _X(-2, 2)) = 10 , l_21 = h^1(X, L_2 ⊗L_1^*) = h^1(X, _X(2, -2))=0 , where $l_ij ≡h^1(X, L_i ⊗L_j^*)$ are the number of arrows from node $j$ to $i$.

Exploring Positive Monad Bundles And A New Heterotic Standard Model · A Rank-2 Example: $SU(2) →S[U(1) ×U(1)]$ · 0.93

Uses data or values from 1 paper

In Ref. [ref] , the DT invariant has been obtained from this as DT(X,c = (2, (0,0), (-4,6), 0 ) ; ω= t^1 J_1 + t^2 J_2 ) = -10 , if $4< t^2/t^1 < ∞$ , 0 , if $0<t^2/t^1 ≤4$ , which is seen to jump when one crosses the stability wall of [ref].

Transitions in the Web of Heterotic Vacua · A Rank-2 Example: $SU(2) →S[U(1) ×U(1)]$ · 0.95

Cites as support 4 papers

It has indeed been shown that when the bundle is decomposed completely into Abelian pieces, the bundle moduli on the wall are subject to the D-term and F-term constraints [ref] ; a crucial observation is that the stability and holomorphicity parts in the HYM equations, Eq. [ref], correspond respectively to the D-terms and F-terms.

The Edge Of Supersymmetry: Stability Walls in Heterotic Theory · Two Perspectives on D-Terms · 0.97
It has indeed been shown that when the bundle is decomposed completely into Abelian pieces, the bundle moduli on the wall are subject to the D-term and F-term constraints [ref] ; a crucial observation is that the stability and holomorphicity parts in the HYM equations, Eq. [ref], correspond respectively to the D-terms and F-terms.

Stability Walls in Heterotic Theories · Two Perspectives on D-Terms · 0.97
It has indeed been shown that when the bundle is decomposed completely into Abelian pieces, the bundle moduli on the wall are subject to the D-term and F-term constraints [ref] ; a crucial observation is that the stability and holomorphicity parts in the HYM equations, Eq. [ref], correspond respectively to the D-terms and F-terms.

Stabilizing the Complex Structure in Heterotic Calabi-Yau Vacua · Two Perspectives on D-Terms · 0.97

Cites as background 14 papers

Along this vein of thought, the quiver description has recently been used to determine BPS spectrum of a given $=2$ theory [ref] , and more direct exploration of the cohomology structure of the quiver variety has also been undertaken (mainly) for Abelian quivers (possibly involving loops) in the context of wall-crossing [ref] .

BPS States, Refined Indices, and Quiver Invariants · Introduction, Summary, and Prospectus · 0.80
Along this vein of thought, the quiver description has recently been used to determine BPS spectrum of a given $=2$ theory [ref] , and more direct exploration of the cohomology structure of the quiver variety has also been undertaken (mainly) for Abelian quivers (possibly involving loops) in the context of wall-crossing [ref] .

BPS Quivers and Spectra of Complete N=2 Quantum Field Theories · Introduction, Summary, and Prospectus · 0.80
Along this vein of thought, the quiver description has recently been used to determine BPS spectrum of a given $=2$ theory [ref] , and more direct exploration of the cohomology structure of the quiver variety has also been undertaken (mainly) for Abelian quivers (possibly involving loops) in the context of wall-crossing [ref] .

N=2 Quantum Field Theories and Their BPS Quivers · Introduction, Summary, and Prospectus · 0.80

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