Mirror symmetry by O3-planes

Amihay Hanany; Bo Feng

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Mirror symmetry by O3-planes

Bo Feng, Amihay Hanany

High Energy Physics - Theory · Submitted 12 Apr 2000

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

The authors' main claim We construct the three dimensional mirror theory of SO(2k) and SO(2k+1) gauge groups by using O3-planes.

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We construct the three dimensional mirror theory of SO(2k) and SO(2k+1) gauge groups by using O3-planes. An essential ingredient in constructing the mirror is the splitting of a physical brane (NS-brane or D5-brane) on O3-planes. In particular, matching the dimensions of moduli spaces of mirror pair (for example, the SO(2k+1) and its mirror) there is a D3-brane creation or annihilation accompanying the splitting. This novel dynamical process gives a nontrivial prediction for strongly coupled field theories, which will be very interesting to check by Seiberg-Witten curves. Furthermore, applying the same idea, we revisit the mirror theory of Sp(k) gauge group and find new mirrors which differ from previously known results. Our new result for Sp(k) gives another example to a previously observed fact, which shows that different theories can be mirror to the same theory. We also discussed the phenomena such as "hidden FI-parameters" when the number of flavors and the rank of the gauge group satisfy certain relations, ``incomplete Higgsing'' for the mirror of SO(2k+1) and the ``hidden global symmetry''. After discussing the mirror for a single Sp or SO gauge group, we extend the study to a product of two gauge groups in two different models, namely the elliptic and the non-elliptic models.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We construct the three dimensional mirror theory of SO(2k) and SO(2k+1) gauge groups by using O3-planes.	contribution 0.98	0.96	0.67	asserted 1.00
s1	An essential ingredient in constructing the mirror is the splitting of a physical brane (NS-brane or D5-brane) on O3-planes.	method 0.95	0.58	0.09	asserted 1.00
s2	In particular, matching the dimensions of moduli spaces of mirror pair (for example, the SO(2k+1) and its mirror) there is a D3-brane creation or annihilation accompanying the splitting.	result 0.55	0.76	0.10	asserted 0.99
s3	This novel dynamical process gives a nontrivial prediction for strongly coupled field theories, which will be very interesting to check by Seiberg-Witten curves.	interpretation 0.67	0.53	0.15	asserted 0.67
s4	Furthermore, applying the same idea, we revisit the mirror theory of Sp(k) gauge group and find new mirrors which differ from previously known results.	result 0.54	0.97	0.15	asserted 1.00
s5	Our new result for Sp(k) gives another example to a previously observed fact, which shows that different theories can be mirror to the same theory.	interpretation 0.85	0.71	0.10	asserted 1.00
s6	We also discussed the phenomena such as "hidden FI-parameters" when the number of flavors and the rank of the gauge group satisfy certain relations, ``incomplete Higgsing'' for the mirror of SO(2k+1) and the ``hidden global symmetry''.	result 0.84	0.82	0.06	asserted 0.97
s7	After discussing the mirror for a single Sp or SO gauge group, we extend the study to a product of two gauge groups in two different models, namely the elliptic and the non-elliptic models.	contribution 0.99	0.92	0.07	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.76.

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Original abstract

We construct the three dimensional mirror theory of SO(2k) and SO(2k+1) gauge groups by using O3-planes. An essential ingredient in constructing the mirror is the splitting of a physical brane (NS-brane or D5-brane) on O3-planes. In particular, matching the dimensions of moduli spaces of mirror pair (for example, the SO(2k+1) and its mirror) there is a D3-brane creation or annihilation accompanying the splitting. This novel dynamical process gives a nontrivial prediction for strongly coupled field theories, which will be very interesting to check by Seiberg-Witten curves. Furthermore, applying the same idea, we revisit the mirror theory of Sp(k) gauge group and find new mirrors which differ from previously known results. Our new result for Sp(k) gives another example to a previously observed fact, which shows that different theories can be mirror to the same theory. We also discussed the phenomena such as "hidden FI-parameters" when the number of flavors and the rank of the gauge group satisfy certain relations, ``incomplete Higgsing'' for the mirror of SO(2k+1) and the ``hidden global symmetry''. After discussing the mirror for a single Sp or SO gauge group, we extend the study to a product of two gauge groups in two different models, namely the elliptic and the non-elliptic models.

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How the literature uses it

51 arXiv papers cite this in 115 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 · 75 sentences without a confident label

Builds on it 2 papers

In [ref] , a set of Type IIA brane configurations involving negatively-charged D6-branes were studied alongside their corresponding electric and magnetic theories [ref] – the following section will derive from these the quotient quivers associated to the gauging of flavour subgroups.

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In other words, the $S$-fold CFTs of this class can be obtained by inserting an $S$-duality wall into an appropriate D3 brane segment of the brane systems described in [ref] .

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Note also that the exotic case dubbed $G=USp'(2N)$ is self-dual: $G^∨=G$.] The quiver for $T^σ⃗_ρ⃗(G)$ can be extracted from the brane construction using standard brane moves [ref] and paying attention to the presence of orientifolds [ref] .

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One can be obtained by using the brane construction involving an O3-plane (see [ref] ): 2 - 2-4 - 4 - ⋯- 2k-10 - 2k-10 - 2k-8 -12k-8 - 2k-7- 2k-8 - ⋯- 2k-7_6 blue nodes & 7 red nodes- 12k-8 - 2k-8 - 2k-10 - 2k-10- ⋯-4 - 4 -2 - 2 The other can be obtained by using the brane construction involving an O5-plane (see [ref] .

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The mirror theory of this quiver can be determined using brane configurations as in Figure 13 of [ref] ; the quiver diagram is given by [font=] [auto, every node/.style=draw, minimum size=1cm, node distance=1cm];

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According to [ref] , the charges of the O$p$ planes (in unites of the physical D$p$ branes) are given by [equation]

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In units of the physical branes, the RR-charges of the planes are as follows [ref] : [equation] As a remark, the NS-charges of the planes are zero.

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As detailed below, the finite coupling magnetic quivers agree with the results of [ref] .

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With this construction, We can reproduce the results from [ref] .

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The corresponding 3d mirror theory mirrorXeven2, with $p=2$, turns out to be coincident with [ref] with $k=x/2$ and $N=x+2$, as it should be.

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To begin with, recall the -- brane configurations of [ref] supplemented by orientifold 3-planes [ref] , which yield $3$d $=4$ world-volume theories with alternating orthogonal and symplectic gauge groups.

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They are defined in terms of a general set of D3 branes ending on NS5 and D5-branes [ref] , possibly in the presence of O3 planes [ref] .

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The Kraft-Procesi transitions described in [ref] for Lie algebras of type $B$, $C$ and $D$ where based on orthosymplectic quivers and their embedding in Type IIB string theory, introduced in [ref] and further refined in [ref] .

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