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Making manifest the symmetry enhancement for coincident BPS branes
High Energy Physics - Theory · Submitted 16 Jun 1998
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We make this gauge symmetry enhancement manifest by considering the hypermultiplet LEEA which is given by the spacetime N=2 non-linear sigma-model (NLSM) having Q as the target space.
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The abstract, sentence by sentence
We consider g coincident M-5-branes on top of each other, in the KK monopole background Q of multiplicity N. The worldvolume of each M-5-brane is supposed to be given by the local product of the four-dimensional spacetime and an elliptic curve. In the coincidence limit, all these curves yield a single (Seiberg-Witten) hyperelliptic curve, while the gauge symmetry is enhanced to U(N). We make this gauge symmetry enhancement manifest by considering the hypermultiplet LEEA which is given by the spacetime N=2 non-linear sigma-model (NLSM) having Q as the target space. The hyper-K"ahler manifold Q is given by the multicentre Taub-NUT space, which in the coincidence limit amounts to the multiple Eguchi-Hanson (ALE) space Q. The NLSM is most naturally described in terms of the hyper-K"ahler coset construction on SU(N,N)/U(N) in harmonic superspace, by using the auxiliary (in classical theory) N=2 vector superfields as Lagrange multipliers, with FI terms resolving the singularity. The Maldacena limit, in which the hypermultiplet LEEA becomes extended to the N=4 SYM with the gauge group U(N), arises in quantum field theory due to a dynamical generation of the N=2 vector and hypermultipet superfields, when sending the FI terms to zero.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider g coincident M-5-branes on top of each other, in the KK monopole background Q of multiplicity N. | background 0.86 | 0.27 | 0.03 | asserted 0.87 |
| s1 | The worldvolume of each M-5-brane is supposed to be given by the local product of the four-dimensional spacetime and an elliptic curve. | background 0.96 | 0.13 | 0.04 | asserted 0.53 |
| s2 | In the coincidence limit, all these curves yield a single (Seiberg-Witten) hyperelliptic curve, while the gauge symmetry is enhanced to U(N). | result 0.75 | 0.24 | 0.25 | asserted 1.00 |
| s3 | We make this gauge symmetry enhancement manifest by considering the hypermultiplet LEEA which is given by the spacetime N=2 non-linear sigma-model (NLSM) having Q as the target space. | contribution 0.59 | 0.83 | 0.33 | asserted 1.00 |
| s4 | The hyper-K"ahler manifold Q is given by the multicentre Taub-NUT space, which in the coincidence limit amounts to the multiple Eguchi-Hanson (ALE) space Q. | background 0.74 | 0.25 | 0.07 | asserted 1.00 |
| s5 | The NLSM is most naturally described in terms of the hyper-K"ahler coset construction on SU(N,N)/U(N) in harmonic superspace, by using the auxiliary (in classical theory) N=2 vector superfields as Lagrange multipliers, with FI terms resolving the singularity. | method 0.98 | 0.55 | 0.12 | asserted 0.95 |
| s6 | The Maldacena limit, in which the hypermultiplet LEEA becomes extended to the N=4 SYM with the gauge group U(N), arises in quantum field theory due to a dynamical generation of the N=2 vector and hypermultipet superfields, when sending the FI terms to zero. | interpretation 0.77 | 0.29 | 0.26 | asserted 1.00 |
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Original abstract
We consider g coincident M-5-branes on top of each other, in the KK monopole background Q of multiplicity N. The worldvolume of each M-5-brane is supposed to be given by the local product of the four-dimensional spacetime and an elliptic curve. In the coincidence limit, all these curves yield a single (Seiberg-Witten) hyperelliptic curve, while the gauge symmetry is enhanced to U(N). We make this gauge symmetry enhancement manifest by considering the hypermultiplet LEEA which is given by the spacetime N=2 non-linear sigma-model (NLSM) having Q as the target space. The hyper-K"ahler manifold Q is given by the multicentre Taub-NUT space, which in the coincidence limit amounts to the multiple Eguchi-Hanson (ALE) space Q. The NLSM is most naturally described in terms of the hyper-K"ahler coset construction on SU(N,N)/U(N) in harmonic superspace, by using the auxiliary (in classical theory) N=2 vector superfields as Lagrange multipliers, with FI terms resolving the singularity. The Maldacena limit, in which the hypermultiplet LEEA becomes extended to the N=4 SYM with the gauge group U(N), arises in quantum field theory due to a dynamical generation of the N=2 vector and hypermultipet superfields, when sending the FI terms to zero.
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