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Conformal Field Theory

Description: This quiz tests your understanding of Conformal Field Theory, a branch of theoretical physics that studies the properties of physical systems that are invariant under conformal transformations.
Number of Questions: 14
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Tags: conformal field theory mathematical physics
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What is the central charge of a conformal field theory?

  1. The number of independent conformal transformations that leave the theory invariant

  2. The dimension of the conformal group

  3. The number of conserved currents in the theory

  4. The number of primary fields in the theory

Show answer
Correct Option: C
Explanation:

The central charge is a measure of the number of degrees of freedom in a conformal field theory. It is related to the number of conserved currents in the theory, which are the generators of conformal transformations.

What is the conformal anomaly?

  1. The difference between the classical and quantum values of the central charge

  2. The divergence of the stress-energy tensor

  3. The non-conservation of the conformal current

  4. The breaking of conformal symmetry in the presence of matter

Show answer
Correct Option: B
Explanation:

The conformal anomaly is a measure of the breaking of conformal symmetry in a quantum field theory. It is related to the divergence of the stress-energy tensor, which is the generator of conformal transformations.

What is a conformal field?

  1. A field that is invariant under conformal transformations

  2. A field that has a well-defined conformal weight

  3. A field that is a primary field

  4. A field that is a descendant field

Show answer
Correct Option: A
Explanation:

A conformal field is a field that is invariant under conformal transformations. This means that its correlation functions are independent of the choice of conformal coordinate system.

What is a primary field?

  1. A field that has a well-defined conformal weight

  2. A field that is a conformal field

  3. A field that is a descendant field

  4. A field that is a marginal field

Show answer
Correct Option: A
Explanation:

A primary field is a field that has a well-defined conformal weight. This means that its correlation functions transform in a simple way under conformal transformations.

What is a descendant field?

  1. A field that is obtained from a primary field by applying a conformal transformation

  2. A field that has a conformal weight that is not well-defined

  3. A field that is not a conformal field

  4. A field that is a marginal field

Show answer
Correct Option: A
Explanation:

A descendant field is a field that is obtained from a primary field by applying a conformal transformation. It has a conformal weight that is related to the conformal weight of the primary field.

What is a marginal field?

  1. A field that has a conformal weight that is equal to zero

  2. A field that is a primary field

  3. A field that is a descendant field

  4. A field that is not a conformal field

Show answer
Correct Option: A
Explanation:

A marginal field is a field that has a conformal weight that is equal to zero. This means that its correlation functions do not transform under conformal transformations.

What is the Ward identity?

  1. An identity that relates the correlation functions of a conformal field theory to its conformal symmetry

  2. An identity that relates the correlation functions of a conformal field theory to its stress-energy tensor

  3. An identity that relates the correlation functions of a conformal field theory to its central charge

  4. An identity that relates the correlation functions of a conformal field theory to its conformal anomaly

Show answer
Correct Option: A
Explanation:

The Ward identity is an identity that relates the correlation functions of a conformal field theory to its conformal symmetry. It is a powerful tool for studying the properties of conformal field theories.

What is the Zamolodchikov C-theorem?

  1. A theorem that states that the central charge of a conformal field theory is always positive

  2. A theorem that states that the central charge of a conformal field theory is always negative

  3. A theorem that states that the central charge of a conformal field theory is always zero

  4. A theorem that states that the central charge of a conformal field theory is always infinite

Show answer
Correct Option: A
Explanation:

The Zamolodchikov C-theorem is a theorem that states that the central charge of a conformal field theory is always positive. This theorem has important implications for the study of conformal field theories.

What is the Cardy formula?

  1. A formula that relates the central charge of a conformal field theory to its entropy

  2. A formula that relates the central charge of a conformal field theory to its free energy

  3. A formula that relates the central charge of a conformal field theory to its temperature

  4. A formula that relates the central charge of a conformal field theory to its pressure

Show answer
Correct Option: A
Explanation:

The Cardy formula is a formula that relates the central charge of a conformal field theory to its entropy. It is a powerful tool for studying the properties of conformal field theories.

What is the conformal bootstrap?

  1. A method for studying the properties of conformal field theories by using only their conformal symmetry

  2. A method for studying the properties of conformal field theories by using their correlation functions

  3. A method for studying the properties of conformal field theories by using their Ward identities

  4. A method for studying the properties of conformal field theories by using their Zamolodchikov C-theorem

Show answer
Correct Option: A
Explanation:

The conformal bootstrap is a method for studying the properties of conformal field theories by using only their conformal symmetry. It is a powerful tool for studying the properties of conformal field theories.

What is the AdS/CFT correspondence?

  1. A correspondence between a conformal field theory in a flat spacetime and a string theory in an anti-de Sitter spacetime

  2. A correspondence between a conformal field theory in a curved spacetime and a string theory in a flat spacetime

  3. A correspondence between a conformal field theory in a flat spacetime and a string theory in a de Sitter spacetime

  4. A correspondence between a conformal field theory in a curved spacetime and a string theory in an anti-de Sitter spacetime

Show answer
Correct Option: A
Explanation:

The AdS/CFT correspondence is a correspondence between a conformal field theory in a flat spacetime and a string theory in an anti-de Sitter spacetime. It is a powerful tool for studying the properties of conformal field theories and string theories.

What is the Ryu-Takayanagi formula?

  1. A formula that relates the entanglement entropy of a region in a conformal field theory to the area of a minimal surface in the dual AdS spacetime

  2. A formula that relates the entanglement entropy of a region in a conformal field theory to the volume of a minimal surface in the dual AdS spacetime

  3. A formula that relates the entanglement entropy of a region in a conformal field theory to the length of a minimal surface in the dual AdS spacetime

  4. A formula that relates the entanglement entropy of a region in a conformal field theory to the curvature of a minimal surface in the dual AdS spacetime

Show answer
Correct Option: A
Explanation:

The Ryu-Takayanagi formula is a formula that relates the entanglement entropy of a region in a conformal field theory to the area of a minimal surface in the dual AdS spacetime. It is a powerful tool for studying the properties of conformal field theories and AdS/CFT correspondence.

What is the conformal collider?

  1. A theoretical tool for studying the properties of conformal field theories by using high-energy collisions

  2. A theoretical tool for studying the properties of conformal field theories by using low-energy collisions

  3. A theoretical tool for studying the properties of conformal field theories by using non-relativistic collisions

  4. A theoretical tool for studying the properties of conformal field theories by using ultra-relativistic collisions

Show answer
Correct Option: A
Explanation:

The conformal collider is a theoretical tool for studying the properties of conformal field theories by using high-energy collisions. It is a powerful tool for studying the properties of conformal field theories and AdS/CFT correspondence.

What is the conformal window?

  1. A range of values of the coupling constant in a conformal field theory where the theory is conformal

  2. A range of values of the coupling constant in a conformal field theory where the theory is not conformal

  3. A range of values of the coupling constant in a conformal field theory where the theory is marginally conformal

  4. A range of values of the coupling constant in a conformal field theory where the theory is strongly conformal

Show answer
Correct Option: A
Explanation:

The conformal window is a range of values of the coupling constant in a conformal field theory where the theory is conformal. It is a powerful tool for studying the properties of conformal field theories.

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