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duplicates list edited from Number of supersymmetric charge and the meaning of $\cal N$ to Number of supersymmetric charge and the meaning of $\cal N$, What's the ${\cal N}$ for SUSY theories?
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Qmechanic ♦
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Post Closed as "Duplicate" by Qmechanic♦
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Explanation for the $(a,b)$ Notation in Super Conformal Field Theories

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Daniel Vainshtein
Daniel Vainshtein
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In the literature, there are many theories and quantities which I usually seen in the context of conformal field theory that described via the notation of $(a,b);\quad a,b\in\mathbb{N}$$(a,b);\quad a,b\in\mathbb{Z}$
for example:

  1. 6 dimensional (2,0) superconformal field theory (6D (2,0) SCFT)

  2. deforming $\text{CFT}_2$ by a (2,2) quasi-primary operator.

  3. (NS,NS) sector of superstring theory is given by vertex operator in the (-1,-1) picture

what this notation $(a,b)$ is stand for? I know that in $\text{CFT}_2$s the Virasoro generators are coming as two copies one for the right sector and the second for the left sector is. Is $a$ representing the number of extended supersymmetries in the left sector while $b$ on the right? if so, what are (2,0) represents in the the first example treating 6d $CFT$?

In the literature, there are many theories and quantities which I usually seen in the context of conformal field theory that described via the notation of $(a,b);\quad a,b\in\mathbb{N}$
for example:

  1. 6 dimensional (2,0) superconformal field theory (6D (2,0) SCFT)

  2. deforming $\text{CFT}_2$ by a (2,2) quasi-primary operator.

  3. (NS,NS) sector of superstring theory is given by vertex operator in the (-1,-1) picture

what this notation $(a,b)$ is stand for? I know that in $\text{CFT}_2$s the Virasoro generators are coming as two copies one for the right sector and the second for the left sector is $a$ representing the number of extended supersymmetries in the left sector while $b$ on the right? if so what are (2,0) represents in the the first example treating 6d $CFT$?

In the literature, there are many theories and quantities which I usually seen in the context of conformal field theory that described via the notation of $(a,b);\quad a,b\in\mathbb{Z}$
for example:

  1. 6 dimensional (2,0) superconformal field theory (6D (2,0) SCFT)

  2. deforming $\text{CFT}_2$ by a (2,2) quasi-primary operator.

  3. (NS,NS) sector of superstring theory is given by vertex operator in the (-1,-1) picture

what this notation $(a,b)$ is stand for? I know that in $\text{CFT}_2$s the Virasoro generators are coming as two copies one for the right sector and the second for the left sector. Is $a$ representing the number of extended supersymmetries in the left sector while $b$ on the right? if so, what are (2,0) represents in the first example treating 6d $CFT$?

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Daniel Vainshtein
Daniel Vainshtein
  • 562
  • 2
  • 12

Explanation for the $(a,b)$ Notation in Conformal Field Theories

In the literature, there are many theories and quantities which I usually seen in the context of conformal field theory that described via the notation of $(a,b);\quad a,b\in\mathbb{N}$
for example:

  1. 6 dimensional (2,0) superconformal field theory (6D (2,0) SCFT)

  2. deforming $\text{CFT}_2$ by a (2,2) quasi-primary operator.

  3. (NS,NS) sector of superstring theory is given by vertex operator in the (-1,-1) picture

what this notation $(a,b)$ is stand for? I know that in $\text{CFT}_2$s the Virasoro generators are coming as two copies one for the right sector and the second for the left sector is $a$ representing the number of extended supersymmetries in the left sector while $b$ on the right? if so what are (2,0) represents in the the first example treating 6d $CFT$?