[Paper Review] D0-Branes As Confined Quarks

Amir H. Fatollahi|ArXiv.org|May 25, 2000

Black Holes and Theoretical Physics3 references3 citations

TL;DR

This paper investigates whether D0-branes in string theory can model confined quarks and QCD strings via matrix quantum mechanics, showing that the inter-D0-brane potential yields a linear confining potential analogous to QCD. It further explores large-N behavior, whiteness of bound states, and the role of non-commutativity in relative distances, suggesting a potential duality between D0-brane dynamics and QCD at strong coupling.

ABSTRACT

The possibility of using the quantum mechanics of D0-branes for the bound-states of quarks and QCD strings is investigated. Issues such as the inter D0-branes potential, the whiteness of the D0-branes bound-states and the large-N limit of D0-branes effective theory are studied. A possible role of the non-commutativity of relative distances of D0-branes in a study of ordinary QCD is discussed.

Motivation & Objective

• To explore whether D0-brane dynamics in matrix quantum mechanics can effectively describe bound states of quarks and QCD strings.
• To compare the inter-D0-brane potential with phenomenological and electric flux models of confinement.
• To analyze the whiteness of D0-brane bound states under SU(N) gauge symmetry.
• To study the large-N limit of D0-brane systems and its relevance to QCD baryons.
• To investigate the potential role of non-commutativity in relative distances of D0-branes for modeling ordinary QCD.

Proposed method

• Formulate the dynamics of N D0-branes using matrix quantum mechanics derived from dimensional reduction of U(N) gauge theory to 0+1 dimensions.
• Use the action $ S = \int dt\; m_0 \text{Tr} \left( \frac{1}{2} D_t X_i^2 + \frac{[X_i, X_j]^2}{4(2\pi\alpha')^2} \right) $, with $ D_t = \partial_t - i[a_0, \cdot] $, to describe the system.
• Compute the one-loop effective potential between two static D0-branes using the trace-log formula for the determinant of the fluctuation operator.
• Identify the light-cone frame interpretation with $ m_0 = p^+ $, $ t = x^+ $, and $ X_i $ as transverse coordinates.
• Apply scaling transformations $ t \to g_s^{-1/3}t $, $ a_0 \to g_s^{1/3}a_0 $, $ X \to g_s^{1/3}X $ to extract physical energy and length scales.
• Relate the fundamental scale $ l_{d+2} = g_s^{1/3}l_s $ to the QCD scale $ \Lambda_{\text{QCD}} $ for $ d=2 $.

Experimental results

Research questions

• RQ1 Can the inter-D0-brane potential reproduce the linear confining potential seen in QCD and the electric flux tube model?
• RQ2 Are bound states of D0-branes white under the SU(N) gauge group, as required for baryons?
• RQ3 How does the large-N limit of the D0-brane system compare with the large-N limit of QCD baryons?
• RQ4 To what extent can non-commutativity of relative distances between D0-branes mimic non-Abelian gauge structure in QCD?
• RQ5 Can the lattice continuum limit in gauge theories be analogously realized in non-commutative D0-brane systems?

Key findings

• The one-loop effective potential between two static D0-branes yields a linear potential $ V(r) \sim 4\pi \left(\frac{d-1}{2}\right) |r| $, matching the confining behavior of QCD.
• The energy scale of the system is $ E \sim g_s^{1/3}/l_s $, consistent with the 4D QCD scale $ \Lambda_{\text{QCD}} $ when $ d=2 $.
• The large-N limit of D0-brane bound states exhibits behavior analogous to QCD baryons, supporting the duality proposal.
• The non-commutativity of D0-brane coordinates arises only in relative distances, not in center-of-mass motion, suggesting a natural confinement mechanism.
• The continuum limit of lattice gauge theories is approached only at zero coupling, implying a deep connection to non-commutative geometry in the strong coupling regime.
• The structure of non-commutative space can mimic non-Abelian gauge theories, as seen in the U(1) gauge theory on non-commutative space becoming interacting, similar to non-Abelian theories.