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Generally, an enhanced gauge symmetry refers to the appearance of gauge theory with a larger gauge group than may be superficially apparent.
A famous case is the enhanced gauge symmetry in the Chan-Paton gauge fields of coincident D-branes. A priori each D-brane carries a complex line bundle/circle principal bundle, but as $n$ of them coincide the gauge group is expected to enhance from $(U(1))^n$ to the unitary group $U(n)$ (or the special unitary group $SU(n)$).
Mathematically this gauge enhancement on D-branes is modeled by the Baum-Douglas geometric cycle model for K-homology (Reis-Szabo 05, def. 1.5 and p. 16, Szabo 08, p. 4): One such cycle is given by a submanifold $W \overset{\phi}{\hookrightarrow} X$ of spacetime $X$ equipped with spin^c structure and with a complex vector bundle $E \to X$, and given two such cycles $(W,\phi,E_1)$ and $(W,\phi,E_2)$ with the same underlying manifold (“coincident D-brane worldvolume”) then their formal direct sum is identified with the single cycle carrying the direct sum of vector bundles
If here $E_i$ has rank $n_i$ and hence structure group $U(n_i)$, then the direct sum of vector bundles $E_1 \oplus E_2$ has structure group the product group $U(n_1) \times U(n_2)$.
In particular the sum of $n$ coincident cycles each carrying a line bundle yields a rank-$n$ vector bundle with structure group $(U(1))^n$. In this sense then a cycle carrying a general rank $n$-vector bundle, hence with structure group $U(n)$, may be thought of as a “gauge enhancement” of making $n$ D-branes coincide.
In the context of the realization of super Yang-Mills theories as effective field theories of superstring theory, BPS branes in the string background becomes BPS states of the SYM theory. These become massless as the cycles on which the BPS charge is supported shrink away (at boundary points of the given moduli space). In this case these additional massless states may appear as additional gauge bosons in the compactified gauge theory which thereby develops a larger gauge group. Typically a previously abelian gauge group becomes non-abelian this way.
Examples include KK-compactification of M-theory on K3 fibers and on G2-manifolds with ADE singularities, corresponding to F-theory on elliptic fibrations making K3-fibrations with singular fibers, corresponding to heterotic string theory on singular elliptic fibrations. See at
M-theory on G2-manifolds the section Nonabelian gauge groups and chiral fermions at orbifold singularities;
F-theory the section F-brane scan
The blow-up of an ADE-singularity is given by a union of Riemann spheres that touch each other such as to form the shape of the Dynkin diagram whose A-D-E label corresponds to that of the given finite subgroup of SU(2).
This statement is originally due to (duVal 1934 I, p. 1-3 (453-455)). A description in terms of hyper-Kähler geometry is due to Kronheimer 89a.
Quick survey of this fact is in Reid 87, a textbook account is Slodowy 80.
In string theory this fact is interpreted in terms of gauge enhancement of the M-theory-lift of coincident black D6-branes to an MK6 at an ADE-singularity (Sen 97):
graphics grabbed from HSS18
See at M-theory lift of gauge enhancement on D6-branes for more.
In Horava-Witten theory there is supposed to be gauge enhancement over the M9-branes such as to identify their worldvolume theory with E8-heterotic string theory.
Under the duality between M-theory and type IIA string theory the M9-brane may be identified with the O8-plane:
from GKSTY 02, section 3
This may be used to understand the gauge enhancement to E8-gauge groups at the heterotic boundary of Horava-Witten theory:
from GKSTY 02, section 3
The idea that on $N$ coincident D-branes there is gauge enhancement to $U(N)$-gauge field theory is due to
There, this is called an “obvious guess” (first line on p. 8). Subsequently, most authors cite this obvious guess as a fact; for instance the review
Discussion in terms of boundary conformal field theory is in
By actual computation in open string field theory “convincing evidence” for the nonabelian Yang-Mills theory on coincident D-branes was found, numerically, in (see bottom of p. 22)
Similar numerical derivation, as well as exact derivation at zero momentum, is in
The first full derivation seems to be due to
which is surveyed in
That on D0-branes this reproduces the BFSS matrix model and on D(-1)-branes the IKKT matrix model is shown in
Discussion of gauge enhancement on coincident D-branes in terms of Baum-Douglas geometric cycles for K-homology is in
reviewed in
Derivation via rational parameterized stable homotopy theory applied to The brane bouquet is in
The picture of M-theory lift of gauge enhancement on D6-branes is due to
Review of the standard lore of gauge enhancement in M-theory includes
(…)
Original articles include
Edward Witten, section 4.6 of String Theory Dynamics In Various Dimensions, Nucl.Phys.B443:85-126,1995 (arXiv:hep-th/9503124)
Chris Hull, Paul Townsend, Enhanced Gauge Symmetries in Superstring Theories, Nucl.Phys. B451 (1995) 525-546 (arXiv:hep-th/9505073)
Paul Aspinwall, Enhanced Gauge Symmetries and K3 Surfaces, Phys.Lett. B357 (1995) 329-334 (arXiv:hep-th/9507012)
Chris Hull, Duality, Enhanced Symmetry and Massless Black Holes, in Proceedings of Strings’95: Future Perspectives in String Theory (World Scientific, 1996, I. Bars et al. eds.), p. 230 (pdf)
M. Bershadsky, Ken Intriligator, Shamit Kachru, David Morrison, V. Sadov, Cumrun Vafa, Geometric Singularities and Enhanced Gauge Symmetries, Nucl.Phys.B481:215-252,1996 (arXiv:hep-th/9605200)
Philip Candelas, Eugene Perevalov, Govindan Rajesh, Toric Geometry and Enhanced Gauge Symmetry of F-Theory/Heterotic Vacua, Nucl.Phys. B507 (1997) 445-474 (arXiv:hep-th/9704097)
Mirjam Cvetic, Chris Hull, Wrapped Branes and Supersymmetry, Nucl.Phys.B519:141-158,1998 (arXiv:hep-th/9709033)
Bobby Acharya, Sergei Gukov, M theory and Singularities of Exceptional Holonomy Manifolds, Phys.Rept.392:121-189,2004 (arXiv:hep-th/0409191)
James Halverson, David Morrison, On Gauge Enhancement and Singular Limits in $G_2$ Compactifications of M-theory (arXiv:1507.05965)
Neil Lambert, Miles Owen, Charged Chiral Fermions from M5-Branes (arXiv:1802.07766)
Discussion via duality of M9-branes to O-planes is in
Last revised on October 8, 2018 at 10:43:41. See the history of this page for a list of all contributions to it.