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Moduli Space Dimensions of Multi-Pronged Strings

Dongsu Bak, Koji Hashimoto, Bum-Hoon Lee, Hyunsoo Min, Naoki Sasakura

TL;DR

This work analyzes 1/4 BPS junctions in ${\cal N}=4$ ${\rm SU}(N)$ SYM to count bosonic and fermionic zero modes around multi-pronged string solutions, and compares the results to the IIB string theory picture. The authors derive the BPS equations ${\bf B}={\bf D}A_4$, ${\bf E}={\bf D}X$ with gauge $A_0=X$, construct the moduli-space metric and connection, and obtain explicit counts: ${\#\rm BZM}={\#\rm monopole}\times 4 - \tilde{N} + 2$ and ${\#\rm FZM}={\#\rm monopole}\times 8 - 4(\tilde{N}-2)$. The fermionic zero modes agree with the IIB description, while the bosonic zero modes exhibit a discrepancy attributed to the field-theoretic softness of monopole configurations along the D3-brane worldvolume, indicating subtle differences in moduli dynamics between the two frameworks. The results motivate further study of supersymmetric quantum mechanics on the moduli space and cross-checks with alternative setups such as M-theory or D-string worldsheet approaches.

Abstract

The numbers of bosonic and fermionic zero modes of multi-pronged strings are counted in ${\cal N}=4$ super-Yang-Mills theory and compared with those of the IIB string theory. We obtain a nice agreement for the fermionic zero modes, while our result for the bosonic zero modes differs from that obtained in the IIB string theory. The possible origin of the discrepancy is discussed

Moduli Space Dimensions of Multi-Pronged Strings

TL;DR

This work analyzes 1/4 BPS junctions in SYM to count bosonic and fermionic zero modes around multi-pronged string solutions, and compares the results to the IIB string theory picture. The authors derive the BPS equations , with gauge , construct the moduli-space metric and connection, and obtain explicit counts: and . The fermionic zero modes agree with the IIB description, while the bosonic zero modes exhibit a discrepancy attributed to the field-theoretic softness of monopole configurations along the D3-brane worldvolume, indicating subtle differences in moduli dynamics between the two frameworks. The results motivate further study of supersymmetric quantum mechanics on the moduli space and cross-checks with alternative setups such as M-theory or D-string worldsheet approaches.

Abstract

The numbers of bosonic and fermionic zero modes of multi-pronged strings are counted in super-Yang-Mills theory and compared with those of the IIB string theory. We obtain a nice agreement for the fermionic zero modes, while our result for the bosonic zero modes differs from that obtained in the IIB string theory. The possible origin of the discrepancy is discussed

Paper Structure

This paper contains 6 sections, 51 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Multi-Pronged Strings and Their Moduli Space
  3. Counting the Number of Zero Modes
  4. Comparison with IIB String Theory
  5. Conclusion
  6. The Normalizability Condition

Figures (2)

  • Figure 1: The configuration of D-string ending on D3-branes is depicted. The figure is for magnetic charges $(m_1,m_2)=(1,1)$ in $SU(3)$ case. The moduli-space is four dimensional.
  • Figure 2: The configuration of pronged strings ending on D3-branes which corresponds to our field theory analysis. The long strings have R-R charge one and small NS-NS charges. The figure is for magnetic charges $(m_1,m_2,m_3)=(1,3,2)$ in $SU(4)$ case.