More Holographic Berezinskii-Kosterlitz-Thouless Transitions

TL;DR

The paper demonstrates two holographic systems—the flavored ABJM theory and a flavored (1,1) little string theory—that exhibit quantum Berezinskii-Kosterlitz-Thouless transitions at nonzero density and magnetic field. The mechanism is an infrared BF-bound violation in an emergent AdS$_2$ region, producing BKT scaling that is erased at any finite temperature, yielding a second-order transition. The authors develop and apply holographic renormalization for probe branes, relate operator normalizations, and compute a substantial portion of the meson spectrum in ABJM, while also framing a generalized-conformal-symmetry criterion for when holographic BKT transitions can arise. They further show analytic and numeric confirmations of BKT behavior, including Efimov-like towers of embeddings and finite-temperature suppression of the BKT scaling, highlighting the limited set of theories where such transitions occur and offering a pathway to understand quantum criticality within holography.

Abstract

We find two systems via holography that exhibit quantum Berezinskii-Kosterlitz-Thouless (BKT) phase transitions. The first is the ABJM theory with flavor and the second is a flavored (1,1) little string theory. In each case the transition occurs at nonzero density and magnetic field. The BKT transition in the little string theory is the first example of a quantum BKT transition in (3+1) dimensions. As in the "original" holographic BKT transition in the D3/D5 system, the exponential scaling is destroyed at any nonzero temperature and the transition becomes second order. Along the way we construct holographic renormalization for probe branes in the ABJM theory and propose a scheme for the little string theory. Finally, we obtain the embeddings and (half of) the meson spectrum in the ABJM theory with massive flavor.

Figures (5)

• Figure 1: A plot of the condensate in the flavored little string theory as a function of magnetic field at zero and finite temperature near the zero-temperature transition. The dashed black line indicates zero-temperature numerical data and the solid blue line our prediction, Eq. (\ref{['cPredict']}). The color dashed curves represent numerical data at background entropy densities of $s=10^{-24}/(2\pi)^4g_s^2R$ (left) and $10^{-22}/(2\pi)^4g_s^2R$ (right). At any nonzero temperature, the condensate scales with a mean-field exponent near the transition and then asymptotes to the BKT scaling at large magnetic field.
• Figure 2: The free energy difference between the broken and symmetric phases of the little string theory as a function of magnetic field. This curve scales exponentially as $\Delta F\sim e^{-2\pi/\alpha}$.
• Figure 3: The density as a function of chemical potential in the broken phase of the little string theory. The thin dashed blue curve represents a direct measurement of the density by Eq. (\ref{['ldVeVs']}) while the thick dashed black curve is $-\partial F/\partial \mu$.
• Figure 4: The rescaled critical horizon radius as a function of $\alpha$ in the little string theory. Over this domain $e^{2\pi/\alpha}$ decreases by a factor $\sim6.64\times 10^6$, while the rescaled radius is relatively constant. The critical radius therefore scales as $r_{h,c}\sim e^{-2\pi/\alpha}$.
• Figure 5: A log-log plot of the condensate as a function of magnetic field at nonzero temperature in the little string theory. The black dots are numerical data and the thin blue line is a fit with slope $.500\sim1/2$. This slope measures the critical exponent $\nu$, which takes the mean-field value.