Softly Broken N=2 QCD With Massive Quark Hypermultiplets, I

We find the phase and flavor symmetry breaking pattern of each N = 1 supersymmetric vacuum of SU (n c ) and U Sp(2n c ) gauge theories, constructed from the exactly solvable N = 2 theories by perturbing them with small adjoint and generic bare hypermultiplet (quark) masses. In SU (n c ) theories with n f ≤ n c the vacua are labelled by an integer r, in which the flavor U (n f ) symmetry is dynamically broken to U (r) × U (n f − r) in the limit of vanishing bare hyperquark masses. In the r = 1 vacua the dynamical symmetry breaking is caused by the condensation of magnetic monopoles in the n f representation. For general r, however, the monopoles in the n f C r representation, whose condensation could explain the flavor symmetry breaking but would produce too-many Nambu-Goldstone multiplets, actually "break up" into "magnetic quarks": the latter with nonabelian interactions condense and induce confinement and dynamical symmetry breaking. In U Sp(2n c ) theories with n f ≤ n c + 1, the flavor SO(2n f ) symmetry is dynamically broken to U (n f ), but with no description in terms of a weakly coupled local field theory. In both SU (n c ) and U Sp(2n c ) theories, with larger numbers of quark flavors, besides the vacua with these properties, there exist also vacua in free magnetic phase, with unbroken global symmetry.

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“…11 One thus finds for the number of vacua 12) which is indeed the correct vacuum multiplicity in this case (Eq. (3.23)).…”

Section: Su(n C )mentioning

confidence: 83%

Dynamical symmetry breaking in supersymmetric and gauge theories

2000

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“…In the physics literature, these additional fields are called massless monopoles, and their number is denoted by 2N f , where 0 Ä N f Ä 4. The case where N f D 0 corresponds to the original SO.3/-Donaldson invariants 1 . The corresponding moduli spaces and invariants when N f > 0 have not been given much consideration in mathematics.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

SO(3)–Donaldson invariants of ℂP²and mock theta functions

Malmendier

Ono

2012

Geom. Topol.

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We compute the Moore-Witten regularized u-plane integral on CP 2 , and we confirm the conjecture that it is the generating function for the SO.3/-Donaldson invariants of CP 2 . We also derive generating functions for the SO.3/-Donaldson invariants with 2N f massless monopoles using the geometry of certain rational elliptic surfaces (N f 2 f0; 2; 3; 4g), and we show that the partition function for N f D 4 is nearly modular. Our results rely heavily on the theory of mock theta functions and harmonic Maass forms (for example, see Ono [40]). 57R57

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“…One may notice that the differentials λ 2nv Dn do not look like those obtained in [6,34,23]. Our next task is to show that they are indeed derived from the N f = 4 SW differentials in spinors of SO (8) and their residues transform in the spinor representation of SO(2N f ) with N f ≤ 3.…”

Section: Spinor Representationmentioning

confidence: 91%

“…Since 34) one has to take care of the total derivative term in ∂λ 8v /∂z (see (A.15)) when converting…”

Section: The D 4 Theorymentioning

confidence: 99%

N = 2 superconformal field theory with ADE global symmetry on a D3-brane probe

1999

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We study mass deformations of N = 2 superconformal field theories with ADE global symmetries on a D3-brane. The N = 2 Seiberg-Witten curves with ADE symmetries are determined by the Type IIB 7-brane backgrounds which are probed by a D3-brane. The Seiberg-Witten differentials λ for these ADE theories are constructed. We show that the poles of λ with residues are located on the global sections of the bundle in an elliptic fibration. It is then clearly seen how the residues transform in an irreducible representation of the ADE groups. The explicit form of λ depends on the choice of a representation of the residues. Nevertheless the physics results are identical irrespective of the representation of λ. This is considered as the global symmetry version of the universality found in N = 2 Yang-Mills theory with local ADE gauge symmetries. *

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Softly Broken N=2 QCD With Massive Quark Hypermultiplets, I

Cited by 46 publications

References 38 publications

Dynamical symmetry breaking in supersymmetric and gauge theories

Dynamical symmetry breaking in supersymmetric and gauge theories

SO(3)–Donaldson invariants of ℂP²and mock theta functions

N = 2 superconformal field theory with ADE global symmetry on a D3-brane probe

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Softly Broken N=2 QCD With Massive Quark Hypermultiplets, I

Cited by 46 publications

References 38 publications

Dynamical symmetry breaking in supersymmetric and gauge theories

Dynamical symmetry breaking in supersymmetric and gauge theories

SO(3)–Donaldson invariants of ℂP2and mock theta functions

N = 2 superconformal field theory with ADE global symmetry on a D3-brane probe

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Product

Resources

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SO(3)–Donaldson invariants of ℂP²and mock theta functions