Developments

Question 1

What is a modulus?

Answer 1

A free parameter (=it lives in a dimension without any potential). Moduli span moduli space.

Question 2

What is the Einstein-Hilbert action?

Answer 2

The action that yields the Einstein field equations from Hamilton’s principle. S=1/2\kappa \int R \sqrt {-g}d^4x,

Question 3

Electric fields appear as ___ in the dual world.

Answer 3

boosts

Question 4

Magnetic fields appear as ____ in the dual world

Answer 4

rotations

Question 5

To obtain the constraints on covariant strings we must impose that…

Answer 5

… the stress energy tensor is zero as an operator

Question 6

What fixes the dimensionality in Polyakov formalism?

Answer 6

The ghost (b,c) field.

Question 7

AdS/CFT correspondence suggests that it is possible to describe a force in quantum mechanics (like electromagnetism, the weak force or the strong force) in a certain number of dimensions (for example four) with a string theory where the strings exist in an anti-de Sitter space, with ____.

Answer 7

one additional (non-compact) dimension

Question 8

What is the fancy name for local scale invariance?

Answer 8

Weyl invariance. This holds for two-dimensional conformal field theory describing the world sheet of a string

Question 9

The Polyakov string action is classically equivalent to ___

Answer 9

the Nambu-Goto string action

Question 10

Just like for transverese Virasoro operators in the light-cone gauge, all positively moded Virasoro operators must… (about physical states)

Answer 10

annihilate physical states. (Physical states must be admissable (being primaries (annihilated by all positively moded Virasoro operators) and annihilated by L_0-1), and not a descendent (linear products of negatively moded Virasoro opertators)

Question 11

Physical states (h=1) fulfill two conditions, which?

Answer 11

1. It is admissable (L_n+\delta_n,0)|state>=0 n>=0

2. It is NOT a descendent (a linear product of negatively moded Virasoro operators)

Question 12

Admissible states are both ___ and ___.

Answer 12

primaries, annihilated by L_0-1

Question 13

The Polyakov string is made conformal (Weyl) invariant through introducing ___ in the Faddeev-Popov procedure. This sets D to 26. Then, a is set to -1 since the gauge invariance in the low energy field theory only works if D=26 and a=-1.

Answer 13

anti-commuting ghost fields

Question 14

What is a genus?

Answer 14

A genus g is the number of holes in any two-dimensional surface without boundaries. The Euler number Chi=2-2g.

Question 15

How is the Euler number defined?

Answer 15

Chi=2-2g.

Question 16

For the Polyakov action to include supergravity the Lagrangian has to produce the ____. This is the relativistic field equation of spin-3/2 fermions. It is similar to the Dirac equation for spin-1/2 fermions.

Answer 16

Rarita-Schwinger equation

Question 17

Massless vector fields become massive (Higgs mechanism) when ____

Answer 17

D-branes move away

Question 18

A Dp-brane has a ___ living on its world-volume, and a ___ for each normal direction.

Answer 18

Maxwell field, massless scalar

Question 19

How many directions have at least one Neumann endpoint condition on a Dp-branes?

Answer 19

p

Question 20

When are the Robin boundary conditions applicable?

Answer 20

When considering a D-brane with electromagnetic field.

Question 21

Born-Infeld theory solves the ___ problem in electrodynamics

Answer 21

infinite self-energy

Question 22

What is the Swampland program?

Answer 22

An aim to extract physics from quantum gravity by finding conditions (so called conjectures). Some examples are: gravity is the weakest force, there are no global symmetries, there are no stable (or semi-stable) de Sitter solutions at all.