More on 8D nonsupersymmetric branes and heterotic strings

We determine the maximal gauge groups arising in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>E</a:mi> <a:mn>8</a:mn> </a:msub> </a:math> heterotic string theory on <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msup> <c:mi>T</c:mi> <c:mn>2</c:mn> </c:msup> </c:math> . Our analysis proceeds along two approaches. First, we start the moduli space of the supersymmetric heterotic string theory on <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi>T</e:mi> <e:mn>2</e:mn> </e:msup> </e:math> focusing on points of maximal gauge enhancement. At these special points, the charge lattice can exhibit a <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi mathvariant="double-struck">Z</g:mi> <g:mn>2</g:mn> </g:msub> </g:math> outer automorphism corresponding to the bulk gauge symmetry. By orbifolding the worldsheet theory by it with the fermion parity, we obtain the maximal gauge group of the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:msub> <j:mi>E</j:mi> <j:mn>8</j:mn> </j:msub> </j:math> theory. Second, we directly study the toroidal compactification of 10D <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:msub> <l:mi>E</l:mi> <l:mn>8</l:mn> </l:msub> </l:math> heterotic string. Both approaches agree, yielding a classification of 22 maximal gauge groups. For each case, we present the corresponding massless spectrum. In light of the no global symmetry/cobordism conjecture in quantum gravity, our result also offers a classification of nonsupersymmetric branes in 8D supersymmetric heterotic string theories.