Landscape of superconducting membranes (0901.1160v2)

Abstract: The AdS/CFT correspondence may connect the landscape of string vacua and the `atomic landscape' of condensed matter physics. We study the stability of a landscape of IR fixed points of N=2 large N gauge theories in 2+1 dimensions, dual to Sasaki-Einstein compactifications of M theory, towards a superconducting state. By exhibiting instabilities of charged black holes in these compactifications, we show that many of these theories have charged operators that condense when the theory is placed at a finite chemical potential. We compute a statistical distribution of critical superconducting temperatures for a subset of these theories. With a chemical potential of one milliVolt, we find critical temperatures ranging between 0.24 and 165 degrees Kelvin.

Analysis of AdS/CFT Correspondence and Superconductivity in M Theory

The paper authored by Frederik Denef and Sean A. Hartnoll presents an in-depth investigation into the interplay between the AdS/CFT correspondence and superconducting phases in theories derived from M theory compactifications. This exploration explores the stability of IR fixed points in 2+1 dimensional gauge theories, specifically those associated with Sasaki-Einstein compactifications. The focus is on understanding how these points transform under finite chemical potentials, leading to conditions that could induce a superconducting state.

Key Insights and Numerical Highlights

The paper establishes a bridge between the string landscape and potential realms of condensed matter physics via gravitational duals provided by the AdS/CFT correspondence. The principal finding is that many 2+1 dimensional large $N$ gauge theories, dual to Sasaki-Einstein spaces, exhibit superconducting instabilities when subjected to finite chemical potentials. The numerical results reveal a broad spectrum of critical superconducting temperatures ranging from 0.24 to 165 Kelvin when the chemical potential is set to one milliVolt. This variation underscores the richness in the landscape of theoretically feasible models, which probably mimic dynamical phenomena observed in condensed matter systems.

Theoretical and Practical Implications

The paper posits that this string landscape could offer a wealth of holographically dual quantum critical theories, potentially enriching our conceptual toolset to describe phenomena like quantum phase transitions in table-top atomic systems or optical lattices. The implications are multi-faceted: from providing new insights into black hole physics by identifying instabilities linked to lower-dimensional black holes, to exploring theoretical models that can simulate superconductivity in materials.

The theoretical backbone of this paper is based in part on the weak gravity conjecture, suggesting that any consistent theory of quantum gravity should allow for the decay of extremal black holes. This leads to an abundance of charged operators and ensuing instabilities when such systems are explored in the context of gravitational dynamics.

Future Developments

The findings invite further exploration into more complex flux compactifications and their stability landscapes in higher or varied dimensions. Furthermore, identifying these analogues in existing or engineered condensed matter systems might push experimental frontiers, opening pathways to simulate these theoretical predictions.

From a theoretical perspective, it encourages the refinement of non-perturbative techniques in AdS/CFT to analyze arbitrary flux backgrounds, coupling instabilities, and extending to broader classes of matter couplings beyond minimal scalar fields. Exploring applications in AdS$_5$/CFT$_4$, analyzing broader metric deformations like p-wave or d-wave superconductors, and ultimately, understanding the detailed nature of transitions at both weak and strong coupling limits constitute vital future challenges.

Moreover, the connectivity woven between speculatively large N quantum field theories and experimentally realizable constructs aligns with ongoing quests in physics to identify and harness fundamental principles in practical settings.

In summary, this research paper contributes profoundly to the theoretical understanding of superconductivity from a holographic viewpoint, while aligning with empirical phenomena in condensed matter physics. It not only uncovers a spectrum of parameter-dependent superconducting transitions in stringy setups but encourages a reimagining of foundational physics through a comprehensive AdS/CFT analysis.