Constraints on the BPS spectrum of N = 2, D = 4 theories with ADE flavor symmetry

Abstract

BPS states of N = 2, D = 4 Super Yang-Mills theories with ADE flavor symmetry arise as junctions joining a D3-brane to a set of 7-branes defining the enhanced flavor algebra. We show that the familiar BPS spectrum of SU(2) theories with N f ≤ 4 is simply given by the set of junctions whose self-intersection is bounded below as required by supersymmetry. This constraint, together with the relations between junction and weight lattices, is used to establish the appearance of arbitrarily large flavor representations for the case of D n≥5 and E n symmetries. Such representations are required by consistency with decoupling down to smaller flavor symmetries.

Five-brane BPS states in heterotic M-theory

“…Comparing this to (4.43), it was shown in [26,27] that a state will be BPS saturated if and only if n 1 , n 2 , n 3 , n 4 take the values The six BPS states in the first row combine to form a triplet of N = 2 hypermultiplets, each of electric charge Q e = 1 and vanishing magnetic charge, in the M 4 worldvolume theory of the wrapped five-brane. We denote these hypermultiplets by Φ i (1,0) , where i = 1, 2, 3.…”

“…This is accomplished by demonstrating the equivalence, in this context, of degenerating M membranes to string junctions, and using the junction lattice techniques developed in [26,27]. …”

“…These are the fundamental objects that compose string junction lattices [26,27], which we review briefly in the Appendix. Furthermore, the self-intersection number of class v given in (4.9) coincides with the norm of the string v defined in [26].…”

“…The low energy theory that arises in the neighborhood of an I * 0 fiber is the same as that of an N = 2, SU(2) Yang-Mills theory with four quark flavors. The BPS multiplets in the I * 0 case can be easily found by comparing to Yang-Mills theory results [29,30], or by using string junctions as in [27]. The results are summarized in the Table 3: The BPS multiplets associated with a fiber of Kodaira type I * 0 .…”

“…However, it turns out that I * 0 multiplets with different (p, q) charges transforming in the same representation of SO (8), transform as different representations of the exceptional groups of the Kodaira fibers III * and IV * . For example [27], the 8 v appearing for the I * 0 fiber with charges (p, q) = (1, 0) is embedded in a 56 of E 7 , or a 27 of E 6 , while the 8 v with charges (p, q) = (1, 2) is embedded in a 27664 of E 7 , or a 351 of E 6 . Consequently, although the type I * 0 BPS multiplets with (p, q) charges listed in Table 3 are also BPS multiplets of type III * and type IV * fibers, they are classified by an infinite number of different E 7 and E 6 representations.…”