Four-dimensional spectrum generating algebra for superstrings

We present the spectrum generating algebra for the hybrid string with manifest <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="script">N</a:mi> <a:mo>=</a:mo> <a:mn>1</a:mn> </a:math> super Poincaré symmetry in <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msup> <d:mi mathvariant="double-struck">R</d:mi> <d:mrow> <d:mn>3</d:mn> <d:mo>,</d:mo> <d:mn>1</d:mn> </d:mrow> </d:msup> <d:mo>×</d:mo> <d:msup> <d:mi mathvariant="double-struck">R</d:mi> <d:mn>6</d:mn> </d:msup> </d:math> . Our Del-Giudice–Di-Vecchia–Fubini operators establish a one-to-one correspondence with the conventional superstring spectrum, while making its four-dimensional structure manifest. We also discuss part of the antifield spectrum, and introduce a simple realization of the supersymmetry charges involving the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msup> <h:mi mathvariant="double-struck">R</h:mi> <h:mn>6</h:mn> </h:msup> </h:math> directions. As an application, we algebraically compute the helicity partition function. These results provide new tools for analyzing four-dimensional on-shell superspaces and may extend naturally to phenomenologically relevant compactifications.