BOUND STATES OF STRINGS AND p-BRANES

BOUND STATES OF STRINGS AND p-BRANES

October, 1995 | Edward Witten
The paper by Edward Witten explores the existence of bound states of Type II p-branes, particularly focusing on the Type IIB superstring in ten dimensions. The main focus is on the $(m,n)$ strings, which are soliton and bound state strings permuted by $SL(2, \mathbf{Z})$. The space-time coordinates enter the formalism as non-commuting matrices, which is a significant and intriguing aspect of the theory. Witten discusses the $(n,1)$ strings, which are bound states of $n$ fundamental strings with a $D$-string. The mass formula for these strings is derived, and it is shown that the binding energy of an elementary string with a $D$-string to form a $(1,1)$ string is almost 100% efficient. This is explained by the non-abelian gauge theory structure of the $D$-brane world-volume theory. For $(m,n)$ strings with $n>1$, a more elaborate construction is required. The existence of these strings is equivalent to the existence of certain vacua with a mass gap in two-dimensional $N=8$ supersymmetric gauge theory. Witten presents a compelling argument for the existence of these vacua and discusses the topological sectors of the gauge theory. The paper also applies similar methods to other $p$-branes, such as instantons, three-branes, five-branes, and seven-branes, discussing their bound states and the conditions under which they can exist. For example, there are no bound states of Dirichlet three-branes or five-branes with exotic world-volume structure due to anomalies in the corresponding gauge theories. Finally, the paper touches on the Type IIA superstring, where the focus is on the bound states of $D$-branes with themselves, corresponding to vacua with a mass gap in ten-dimensional $SU(n)$ super Yang-Mills theory dimensionally reduced to $p+1$ dimensions. The predictions for small $p$ are discussed, and the limitations of anomaly-based arguments for larger $p$ are noted.The paper by Edward Witten explores the existence of bound states of Type II p-branes, particularly focusing on the Type IIB superstring in ten dimensions. The main focus is on the $(m,n)$ strings, which are soliton and bound state strings permuted by $SL(2, \mathbf{Z})$. The space-time coordinates enter the formalism as non-commuting matrices, which is a significant and intriguing aspect of the theory. Witten discusses the $(n,1)$ strings, which are bound states of $n$ fundamental strings with a $D$-string. The mass formula for these strings is derived, and it is shown that the binding energy of an elementary string with a $D$-string to form a $(1,1)$ string is almost 100% efficient. This is explained by the non-abelian gauge theory structure of the $D$-brane world-volume theory. For $(m,n)$ strings with $n>1$, a more elaborate construction is required. The existence of these strings is equivalent to the existence of certain vacua with a mass gap in two-dimensional $N=8$ supersymmetric gauge theory. Witten presents a compelling argument for the existence of these vacua and discusses the topological sectors of the gauge theory. The paper also applies similar methods to other $p$-branes, such as instantons, three-branes, five-branes, and seven-branes, discussing their bound states and the conditions under which they can exist. For example, there are no bound states of Dirichlet three-branes or five-branes with exotic world-volume structure due to anomalies in the corresponding gauge theories. Finally, the paper touches on the Type IIA superstring, where the focus is on the bound states of $D$-branes with themselves, corresponding to vacua with a mass gap in ten-dimensional $SU(n)$ super Yang-Mills theory dimensionally reduced to $p+1$ dimensions. The predictions for small $p$ are discussed, and the limitations of anomaly-based arguments for larger $p$ are noted.
Reach us at info@study.space