(E) This is the second lecture from Professor Sean Hartnoll from the Stanford Institute of Theoretical Physics, that attempts to articulate some of the properties of Black Holes in order to better understand the “exotic” phases of low-temperature matter such as superconductors.

As I did for Part 1, following are my notes from the lecture and below the video of the lecture:

Key Takeaways from Part 1

“Exotic” materials such as high-temperature superconductors (Tc ~ 100 Kelvin) that are neither ordered (such as a solid) nor disordered (such as gas) are called quantum liquids.

Classical Black Holes have thermodynamic properties such as entropy and when probed behave like a medium where the characteristics time/scale ℏ /T are neither long or short.

Duality

In order to deep dive into the connections between Black Holes and quantum liquids, we will use the concept of duality.

Example of duality in physics

Quantum electrodynamics (QED): electromagnetic field lines between electrons are made of photons. They are floppy. Photons don’t interact very strongly.

Quantum chromodynamics (QCD): electromagnetic field lines between quarks are made of gluons. They very are concentrated forming a “flex tube” that leads to a property called “confinement”. Quarks interact strongly.

Hypothesis (the 1970s) – Origin of String Theory

What if the flex tube itself that can be considered as a “string” between the particles is more “fundamental” than quarks and gluons?

Example of simple duality in algebra:

• Area = ∫ dx dy exp(-x2-y2) = ∫ r dr dθ exp(-r2) = π
  

“Path” Integral

• The flex tube is fundamental and the particles are “derived”?
• The particles are fundamental and the flex tube is “derived”?

“Maldacena” Duality (1997)

Duality between dynamics of the Black Hole horizon and a particular quantum liquid.

This Black Hole is in a theoretical box “warmed” at the Hawking radiation temperature. It differs from Black Holes in the Universe in two ways:

• No radiation goes out to infinity and the Black Hole is charged

As a result:

• Can this quantum liquid becomes superconducting at low temperature?
• Can the Black Hole become superconducting at low temperature?

No-Hair Theorems (John Wheeler)

Nothing can stay outside a Black Hole. An object wants to fall into the Black Hole or radiates off to infinity.

The Condensate Outside the Black Hole

The mechanism for superconductivity is similar to the Higgs boson mechanism. A condensate is a well-defined medium where particles become massive. The Higgs boson condensate gives a mass to the electrons and many other particles. The superconductor condensate gives a mass to the photons.

When a photon acquires a mass, the force between the charges changes from 1/r2 to 1/r2 exp (-mr), and as a result, the photon does not enter the superconducting region.

In a superconductor, resistivity is zero/conductivity is infinite and there is a current without an electric field:

• J =  σ E => σ = J/E => E -> 0 => σ -> ∞

The photon acquiring a mass changes the behavior of the electric field which does not enter the superconductor. This is what gives to the matter its superconducting property.

Schwinger Pair of Production – Screening/Anti-Screening

Electromagnetism wants to screen the field that is reducing the field. Gravity wants to anti-screen the field that is increasing the field. Anti-screening is what has led to the creation of the galaxies and the stars in the Universe.

Application to the theoretical “Black Hole”, used in the Maldacena duality

• At high temperature, the gravity forces win (see part I for equations) and the Black Hole becomes bigger

• At low temperature, the electromagnetic forces win and the Black Hole stays small

As we are lowering the temperature of the Black Hole below Tc, the condensate of charges outside the Black Hole gives its superconducting layer to the Black Hole or no “hair” outside the Black Hole.

Above Tc, the Black Hole is a quantum liquid.

Note: The picture above is Flower Festival: Feast of Santa Anita, a painting from Diego Rivera from New York’s MoMA.

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