Heterotic M(atrix) Strings and Their Interactions

Soo-Jong Rey

TL;DR

The paper extends the DVV nonperturbative M(atrix) description to heterotic strings by compactifying M(atrix) theory on ${\bf S}_1/{\bf Z}_2$ and applying dualities, yielding a second-quantized light-cone heterotic string. In the strong-coupling regime the theory flows to a $(8,0)$ SCFT realized as the $S_N$ symmetric product orbifold, where twisted sectors encode multi-string configurations and the spectrum matches the perturbative heterotic string after appropriate GSO projections. The author identifies a unique leading irrelevant operator of total dimension $3$, arising as a tensor product of left-moving twist descendants and right-moving bosonic twists, which generates cubic joining/splitting interactions and scales with the heterotic coupling $g_H$. This framework reproduces the known cubic vertices in both Green-Schwarz and NSR formulations, providing a nontrivial consistency check, and suggests possible extensions to bosonic strings via dimensional reduction of $d=26$ Yang-Mills.

Abstract

Following recent proposal of Dijkgraaf, Verlinde and Verlinde, we show that the M(atrix) theory compactified on $S_1/Z_2$ provides with a non-perturbative description of second-quantized light-cone heterotic string. This so-called heterotic M(atrix) string theory is defined by two-dimensional (8,0) supersymmetric chiral gauge theory with gauge group SO(2N) in the large N limit. We argue that at strong coupling fixed point the chiral gauge theory flows to a (8,0) superconformal field theory defined via $S_N$ symmetric product space orbifold. We show that the leading order correction to the strong coupling expansion corresponds to a unique irrelevant operator of scaling dimension three and describes joining and splitting cubic interactions of light-cone heterotic string. We also speculate on M(atrix) description of bosonic strings via dimensional reduction of d=26 Yang-Mills theory.

Heterotic M(atrix) Strings and Their Interactions

TL;DR

The paper extends the DVV nonperturbative M(atrix) description to heterotic strings by compactifying M(atrix) theory on

and applying dualities, yielding a second-quantized light-cone heterotic string. In the strong-coupling regime the theory flows to a

SCFT realized as the

symmetric product orbifold, where twisted sectors encode multi-string configurations and the spectrum matches the perturbative heterotic string after appropriate GSO projections. The author identifies a unique leading irrelevant operator of total dimension

, arising as a tensor product of left-moving twist descendants and right-moving bosonic twists, which generates cubic joining/splitting interactions and scales with the heterotic coupling

. This framework reproduces the known cubic vertices in both Green-Schwarz and NSR formulations, providing a nontrivial consistency check, and suggests possible extensions to bosonic strings via dimensional reduction of

Yang-Mills.

Abstract

Following recent proposal of Dijkgraaf, Verlinde and Verlinde, we show that the M(atrix) theory compactified on

provides with a non-perturbative description of second-quantized light-cone heterotic string. This so-called heterotic M(atrix) string theory is defined by two-dimensional (8,0) supersymmetric chiral gauge theory with gauge group SO(2N) in the large N limit. We argue that at strong coupling fixed point the chiral gauge theory flows to a (8,0) superconformal field theory defined via

symmetric product space orbifold. We show that the leading order correction to the strong coupling expansion corresponds to a unique irrelevant operator of scaling dimension three and describes joining and splitting cubic interactions of light-cone heterotic string. We also speculate on M(atrix) description of bosonic strings via dimensional reduction of d=26 Yang-Mills theory.