Basics on strings

Question 1

Relativistic strings are continuous and are therefore…

Answer 1

massless and travelling at the speed of light, perpendicular to the string, at the end points.

Question 2

Embedded functions X, called ___, tell the place of the worldsheet in spacetime. They are maps from the world-sheet to some target space

Answer 2

string coordinates

Question 3

What is the Nambu-Goto action?

Answer 3

The simplest string action functional

Question 4

What is the condition for the orthogonality gauge?

Answer 4

The velocity is orthogonal to the string

Question 5

What is the condition from the static gauge?

Answer 5

X0=c*tau

Question 6

What constraint is imposed by the energy gauge?

Answer 6

Sigma at t=0

Question 7

What three gauges (reparametrisation conditions) produces the wave equation from the Nambu-Goto action?

Answer 7

Static gauge, orthogonality gauge, energy gauge

Question 8

String theory is a 2-dimensional ___ that generates an effective ___ in higher spacetime-dimensions.

Answer 8

QFT, QFT

Question 9

Local symmetries concern the reparametrisation invariance and are determined by ____.

Answer 9

gauge choices

Question 10

What symmetries concern the Poincaré symmetric target space

Answer 10

Global symmetries

Question 11

How is the Regge slope parameter defined?

Answer 11

alpha’=hbar*E^2/J

Question 12

How is the string length defined?

Answer 12

ls=hbarcsqrt(alpha’)

Question 13

Why do we use the light-cone gauge?

Answer 13

To avoid quantisation problems from the fact that the functions (string coordinates) are bilinear (having two arguments)

Question 14

Are the light-cone coordinates Lorentz invariant?

Answer 14

No

Question 15

Only for ____ are the only physical motions perpendicular to the string

Answer 15

relativistic strings

Question 16

Why are relativistic strings sometimes referre to as massless strings?

Answer 16

Because the mass (or rest energy) arises only because the string has a tension

Question 17

What is the dimension of tau and sigma in the light-cone gauge?

Answer 17

They are dimensionless

Question 18

Are there any dimensionless, adjustable parameters in string theory?

Answer 18

No, there aren’t

Question 19

How is the effective string mass defined?

Answer 19

mu_eff=gamma*T_0/c^2

Question 20

These previous gauges simplify enormously but we still have quadratic constraints (the functions are bilinear - they have ___). To avoid quantisation problems we will simplify this by using ___.

Answer 20

two arguments, light-cone coordinates

Question 21

In the light cone gauge, tau is proportional to

Answer 21

X^+

Question 22

From the mode expansion (of the light-cone solutions) we define ____ as half the sum of all the renormalised creation and annihiliation operation products.

Answer 22

the transverse Virasoro generators

Question 23

The ambiguities (such as D and a) produced when defining the quantum theory are fixed (D becoming the critical dimension) by requiring that ___

Answer 23

the theory be Lorentz invariant

Question 24

What is beta for closed strings?

Answer 24

Beta=1

Question 25

Except for shared position and momentum zero modes, the operator content of ____ can be viewed as two commuting copies of the open string operators.

Answer 25

quantum closed strings

Question 26

Where does the level matching condition for closed strings come from?

Answer 26

From alpha_0^-=alphabar_0^- which leads to L_0^perp=Lbar_0^perp

Question 27

___ controls the strength of string interactions.

Answer 27

The dilaton state (this exists in closed string theory)

Question 28

Imposing ___ on closed strings creates two sectors: untwisted (invariant) and twisted (antiperiodic and expressed in half integers: tachyons but no massless fields) closed strings.

Answer 28

Z_2 identification

Question 29

The closed string coupling constant, which is also | the loop counting parameter, comes from ___

Answer 29

the dilaton

Question 30

Two problems with bosonic strings: ___ → unstable, and no spacetime ___. This is solved by adding a fermionic field. If we make these spinors we find the NSR formalism.

Answer 30

tachyon, fermions

Question 31

Superstring theory is space-time supersymmetric, tachyon free, and describes all known massless bosonic and fermionic particles. It is an extension to the ___. The bosonic string coordinates are accompanied by the fermionic coordinates that can be divided into two sectors. The Ramond (Naveu-Schwarz) sector concerns periodic (antiperiodic) boundary conditions and sum over integer (half-integer) modes.

Answer 31

Poincaré algebra

Question 32

From ___ it follows that D=10 for superstrings.

Answer 32

the spacetime Lorentz commutator

Question 33

In the __ sector the space of states transform as spinor representations of SO(8) and we have 8 (fermionic) zero modes. These create 8 ground states with an even number of creation operators (and 8 with odd). These are left and right chiral spinors. They have opposite spin statistic properties.

Answer 33

Ramond

Question 34

This spin statistic (and number counting) problem is solved with the __ which keeps only the left chiral ground states and fermionic states so that R becomes R-. Similarly the NS sector becomes the NS+ sector as the tachyon is eliminated so that only bosonic integer spin fields are left.

Answer 34

GSO projection

Question 35

What type of states are contained in the R sector?

Answer 35

fermionic states

Question 36

The closed superstring has left and right going modes (NS+,NS+), (NS+, R-), (R,NS+), (R,R-) where the tachyon is omitted, the middle two are the ____ fields (spin 3/2 anti-commuting fields for local supersymmetry needed for supergravity).

Answer 36

Rarita-Schwinger

Question 37

Is the NS-sector periodic?

Answer 37

No, it's antiperiodic

Question 38

Type IIB theory contains two scalar fields, the scalar φ(x) and the pseudo-scalar A(x). They appear in the Lagrangian together as a ___, i.e., these two fields can be viewed as coordinates on the coset space SU(1, 1)/U(1) (which is an unbounded Euclidean hyperbolic space familiar from the course in GR).

Answer 38

non-linear sigma-model

Question 39

Type I supergravity theory is obtained from the type | IIB theory by imposing ___ on the closed string.

Answer 39

invariance under orientation reversal