Fractional Branes and Boundary States in Orbifold Theories

Duiliu-Emanuel Diaconescu; Jaume Gomis

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Fractional Branes and Boundary States in Orbifold Theories

High Energy Physics - Theory · Submitted 30 Jun 1999

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

The authors' main claim This suggests that the classification of boundary states provides a sort of "quantum K-theory" just as chiral rings in CFT provide "quantum" generalizations of cohomology.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.26 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.93 · mentions code or data availability 0.02.

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We study the D-brane spectrum of N=2 string orbifold theories using the boundary state formalism. The construction is carried out for orbifolds with isolated singularities, non-isolated singularities and orbifolds with discrete torsion. Our results agree with the corresponding K-theoretic predictions when they are available and generalize them when they are not. This suggests that the classification of boundary states provides a sort of "quantum K-theory" just as chiral rings in CFT provide "quantum" generalizations of cohomology. We discuss the identification of these states with D-branes wrapping holomorphic cycles in the large radius limit of the CFT moduli space. The example C^3/Z_3 is worked out in full detail using local mirror symmetry techniques. We find a precise correspondence between fractional branes at the orbifold point and configurations of D-branes described by vector bundles on the exceptional P^2 cycle.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the D-brane spectrum of N=2 string orbifold theories using the boundary state formalism.	contribution 0.95	0.94	0.05	asserted 0.95
s1	The construction is carried out for orbifolds with isolated singularities, non-isolated singularities and orbifolds with discrete torsion.	contribution 0.67	0.87	0.04	asserted 0.99
s2	Our results agree with the corresponding K-theoretic predictions when they are available and generalize them when they are not.	result 0.97	0.86	0.27	asserted 0.98
s3	This suggests that the classification of boundary states provides a sort of "quantum K-theory" just as chiral rings in CFT provide "quantum" generalizations of cohomology.	interpretation 1.00	0.40	0.39	hedged possibility 1.00
s4	We discuss the identification of these states with D-branes wrapping holomorphic cycles in the large radius limit of the CFT moduli space.	contribution 0.87	0.74	0.07	asserted 0.57
s5	The example C^3/Z_3 is worked out in full detail using local mirror symmetry techniques.	method 0.65	0.91	0.07	asserted 0.99
s6	We find a precise correspondence between fractional branes at the orbifold point and configurations of D-branes described by vector bundles on the exceptional P^2 cycle.	result 1.00	0.95	0.32	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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Original abstract

We study the D-brane spectrum of N=2 string orbifold theories using the boundary state formalism. The construction is carried out for orbifolds with isolated singularities, non-isolated singularities and orbifolds with discrete torsion. Our results agree with the corresponding K-theoretic predictions when they are available and generalize them when they are not. This suggests that the classification of boundary states provides a sort of "quantum K-theory" just as chiral rings in CFT provide "quantum" generalizations of cohomology. We discuss the identification of these states with D-branes wrapping holomorphic cycles in the large radius limit of the CFT moduli space. The example C^3/Z_3 is worked out in full detail using local mirror symmetry techniques. We find a precise correspondence between fractional branes at the orbifold point and configurations of D-branes described by vector bundles on the exceptional P^2 cycle.

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Cited by 14 Pith papers

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How the literature uses it

26 arXiv papers cite this in 39 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 19 sentences without a confident label

Contests it 1 paper

Then one looks at the B-model on the mirror manifold (see [ref] for a review[In [ref] the orbifold point is incorrectly set at $t≠0$.]).

Instantons, Quivers and Noncommutative Donaldson-Thomas Theory · Large radius partition functions · contest 0.71

Uses its method or tool 1 paper

An especially simple and elegant method is the quiver approach [ref] (for previous work see [ref] and the nice review [ref] ) which, for the convenience of the reader, we briefly review in section 2 below.

Half--Hypers and Quivers · Introduction · 0.85

Uses its data or values 1 paper

Substituting into [ref], we get d/dτ [ T; T_D ] = C [ 1; τ ] Using the values $(T,T_D)=(-1/2,1/3)$ at the orbifold point $τ_o$ [ref] we can write the periods as a holomorphic Eichler integral

BPS Dendroscopy on Local $P^2$ · Periods as Eichler integrals · 0.92

Compares with it 2 papers

s↦as+b/cs+d, w↦w/cs+d + as+b/cs+d m - m_D Under the $Γ_1(3)$ transformations τ↦τ+1 , τ↦-τ/3τ-1 , τ↦-τ+1/3τ+2 corresponding to monodromies around $∞$, $0$ and $τ_o$, we find, in agreement with [ref] [This also agrees with [ref] upon conjugating the matrices in by $([ 1 0 0; 1/2 1 0; 0 0 1 ])$, due to a shift $T→T+1/2$.]

BPS Dendroscopy on Local $P^2$ · Monodromies · 0.87
These charges agree with both those of an open string disk amplitude computation and a boundary state analysis for fractional D0-branes [ref] .

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Cites it as background 14 papers

In the last year there has been significant progress in the computation of BPS spectra of 4d $=2$ supersymmetric gauge theories using the Representation Theory of quivers with superpotentials [ref] (for previous work see [ref] ; for other approches to the $=2$ BPS spectra see [ref] ).

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There is a large and interesting class of 4d $=2$ supersymmetric gauge theories [ref] whose BPS spectrum has a quiver description, i.e. their BPS states may be identified with the stable objects of the ($$–linear) Abelian category $𝗋𝖾𝗉(Q,)$ of representations of a (finite) quiver $Q$ bounded by the Jacobian relations $∂=0$; here $$ is the superpotential of a quiver SQM, defined on $Q$, whose supersymmetric vacua correspond to the 4d BPS states (see the recent papers [ref] ; for previous work see [ref] ; for a nice review of the basic theory, see [ref] ).

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We start by recalling that, in this case, there are three different kinds of fractional D3-branes, that we call $D3_frac^0$, $D3_frac^1$ and $D3_frac^2$, with different D7-, D5- and D3-charges [ref] .

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