Superstrings in D=10 from supermembranes in D=11

(p,q)-string in the wrapped supermembrane on 2-torus: A classical analysis of the bosonic sector

“…has been rewritten in Polyakov form by introducing the worldsheet metricγ ij instead of Nambu-Goto form. As is pointed out in [2], this action (2.35) has conformal invariance.…”

“…Actually, we shall see that the (p, q)-string comes out through the double dimensional reduction and T-duality in the next section. Now that we shall adopt the double dimensional reduction technique [2]. However, we should be careful to deduce (p, q)-strings.…”

“…Actually, it was shown that the wrapped supermembrane on R 10 × S 1 is related to type IIA superstring on R 10 by means of the double dimensional reduction [2]. On the other hand, type IIB superstring is related to type IIA superstring via T-duality, or type IIA superstring on R 9 × S 1 leads to type IIB superstring on R 10 in the shrinking limit of the S 1 radius.…”

The SO(32) heterotic and type IIB membranes

“…The current membrane actions could be named the type IIA [1,2] and E 8 [3,4] membranes since their dimensional reduction yields the type IIA and E 8 × E 8 strings, respectively. Recall that the type IIA membrane [1,2] has the topology of a torus, while the E 8 membrane [3,4] has the topology of a cylinder.…”

“…Recall that the type IIA membrane [1,2] has the topology of a torus, while the E 8 membrane [3,4] has the topology of a cylinder. To construct the latter membrane, one needs to invoke anomaly cancellation arguments to justify the coupling of the membrane to an E 8 gauge group at each of its ends.…”