Landscape

Select a theory SU(2): 4 fund + 4 anti-fund (not completed) SU(2): 1 Adj + 1 fund + 1 anti-fund SU(2): 1 Adj + 2 fund + 2 anti-fund (not completed) SU(2): 1 Adj + 3 fund + 3 anti-fund (not completed) SU(2): 2 Adj SU(2): 2 Adj + 1 fund + 1 anti-fund SU(3): 1 Adj + 1 fund + 1 anti-fund SU(3): 1 Adj + 2 fund + 2 anti-fund (not completed) SU(5): 2 rank-2 symm + (conj.) SU(5): 1 rank-2 symm + 1 rank-2 anti-symm + (conj.) SU(5): 1 rank-2 symm + 1 rank-2 anti-symm + 1 fund + (conj.) (not completed) SU(5): 1 rank-2 symm + 1 rank-2 anti-symm + 2 conj. of rank-2 anti-symm + 8 anti-fund (not completed) SU(5): 1 rank-2 symm + 1 rank-2 anti-symm + 2 conj. of rank-2 anti-symm + 1 fund + 9 anti-fund (not completed) SU(5): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 symm SU(5): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 symm + 1 fund + 1 anti-fund SU(5): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 anti-symm + 8 anti-fund (not completed) SU(5): 1 Adj + 1 rank-2 anti-symm + 1 conj. of rank-2 anti-symm SU(5): 1 Adj + 1 rank-2 anti-symm + 1 conj. of rank-2 anti-symm + 1 fund + 1 anti-fund (not completed) SU(5): 1 rank-2 symm + 2 rank-2 anti-symm + (conj.) (not completed) SU(5): 1 rank-2 symm + 2 rank-2 anti-symm + 1 fund + (conj.) (not completed) SU(5): 3 rank-2 anti-symm + (conj.) (not completed) SU(5): 3 rank-2 anti-symm + 1 fund + (conj.) (not completed) SU(5): 2 Adj + 1 anti-symm + 1 conj. of rank-2 anti-symm (not completed) SU(5): 2 Adj + 1 anti-symm + 1 conj. of rank-2 anti-symm + 1 fund + 1 anti-fund (not completed) SU(6): 2 rank-2 symm + (conj.) SU(6): 2 rank-2 symm + 1 fund + (conj.) SU(6): 1 rank-2 symm + 1 rank-2 anti-symm + (conj.) SU(6): 1 rank-2 symm + 1 rank-2 anti-symm + 2 conj. of rank-2 anti-symm + 1 fund + 9 anti-fund (not completed) SU(6): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 symm SU(6): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 anti-symm + 1 fund + 9 anti-fund (not completed) SU(7): 1 rank-2 symm + 2 conj. of rank-2 symm + 1 anti-symm + 8 fund (not completed) SU(7): 2 rank-2 symm + 1 fund + (conj.) (not completed) SU(8): 1 rank-2 symm + 2 conj. of rank-2 symm + 1 anti-symm + 9 fund + 1 anti-fund (not completed) SU(9): 2 rank-2 symm + 2 conj. of rank-2 anti-symm + 16 anti-fund (not completed) SU(9): 2 rank-2 symm + (conj.) (not completed) SU(9): 2 rank-2 symm + 1 fund (conj.) (not completed) SU(10): 2 rank-2 symm + 2 conj. of rank-2 anti-symm + 1 fund + 17 anti-fund (not completed) SO(5): 5 vector (not completed) SO(5): 1 Adj + 1 vector SO(5): 1 Adj + 2 vector SO(5): 1 rank-2 symm SO(5): 1 rank-2 symm + 1 vector SO(5): 1 rank-2 symm + 2 vector Sp(2): 1 Adj + 2 fund Sp(2): 1 14 + 2 fund Sp(2): 2 Adj Sp(2): 1 Adj + 2 rank-2 anti-symm + 8 fund (not completed) G2: 1 Adj + 1 fund E[USp(6)] (not completed) All theories Data used in arXiv:2408.02953

$a$ =

$c$ =

$\leq a \leq$

$\leq c \leq$

id =

Search for theories with rational R-charges and central charges.

Chosen Fixed Point

Here is the data for the chosen fixed point.
$F_{UV}$ represents the flavor symmetries in the UV Lagrangian, and $F_{IR}$ represents the flavor symmetries in the IR. $F_{UV}$ and $F_{IR}$ can differ due to accidental symmetry enhancement.
The number of marginal operators, $n_{marginal}$, minus the dimension of flavor symmetries in IR, $|F_{IR}|$, corresponds to the coefficient of $t^6$ in the superconformal index.

#	Theory	Superpotential	Central charge $a$	Central charge $c$	Ratio $a/c$	Matter field: $R$-charge	U(1) part of $F_{UV}$	Rank of $F_{UV}$	Rational
45880	SU2adj1nf2	${}\phi_{1}q_{1}q_{2}$ + ${ }M_{1}\phi_{1}\tilde{q}_{1}\tilde{q}_{2}$ + ${ }M_{2}q_{2}\tilde{q}_{1}$ + ${ }M_{3}q_{1}\tilde{q}_{2}$	0.6689	0.8346	0.8015	[M:[0.6982, 0.6982, 0.6982], q:[0.8254, 0.8254], qb:[0.4763, 0.4763], phi:[0.3491]]	[M:[[0, -2, -2], [-1, -3, 0], [1, -1, -4]], q:[[-1, 1, 1], [1, 0, 0]], qb:[[0, 3, 0], [0, 0, 3]], phi:[[0, -1, -1]]]	3

Relevant Operators	Marginal Operators	$n_{marginal}$$-$$|F_{IR}|$	Superconformal Index	Refined index
${}M_{2}$, ${ }M_{3}$, ${ }M_{1}$, ${ }\phi_{1}^{2}$, ${ }\tilde{q}_{1}\tilde{q}_{2}$, ${ }\phi_{1}\tilde{q}_{1}^{2}$, ${ }q_{1}\tilde{q}_{1}$, ${ }q_{2}\tilde{q}_{2}$, ${ }\phi_{1}\tilde{q}_{2}^{2}$, ${ }M_{2}^{2}$, ${ }M_{3}^{2}$, ${ }M_{1}M_{3}$, ${ }M_{3}\phi_{1}^{2}$, ${ }M_{1}^{2}$, ${ }M_{2}M_{3}$, ${ }M_{1}\phi_{1}^{2}$, ${ }\phi_{1}^{4}$, ${ }M_{1}M_{2}$, ${ }M_{2}\phi_{1}^{2}$, ${ }M_{3}\tilde{q}_{1}\tilde{q}_{2}$, ${ }q_{1}q_{2}$, ${ }M_{1}\tilde{q}_{1}\tilde{q}_{2}$, ${ }\phi_{1}^{2}\tilde{q}_{1}\tilde{q}_{2}$, ${ }M_{2}\tilde{q}_{1}\tilde{q}_{2}$, ${ }\tilde{q}_{1}^{2}\tilde{q}_{2}^{2}$	${}M_{1}q_{1}\tilde{q}_{1}$, ${ }M_{2}q_{1}\tilde{q}_{1}$, ${ }M_{3}q_{1}\tilde{q}_{1}$, ${ }M_{2}\phi_{1}\tilde{q}_{1}^{2}$, ${ }M_{3}\phi_{1}\tilde{q}_{1}^{2}$, ${ }\phi_{1}^{3}\tilde{q}_{1}^{2}$, ${ }M_{1}q_{2}\tilde{q}_{2}$, ${ }M_{2}q_{2}\tilde{q}_{2}$, ${ }M_{3}q_{2}\tilde{q}_{2}$, ${ }M_{2}\phi_{1}\tilde{q}_{2}^{2}$, ${ }M_{3}\phi_{1}\tilde{q}_{2}^{2}$, ${ }\phi_{1}^{3}\tilde{q}_{2}^{2}$	7	4*t^2.095 + t^2.858 + 4*t^3.905 + 10*t^4.189 + 5*t^4.953 + t^5.716 + 7*t^6. + 20*t^6.284 + 4*t^6.763 + 6*t^7.047 + 6*t^7.811 + 5*t^8.095 + 35*t^8.379 + t^8.574 + 3*t^8.858 - t^4.047/y - (4*t^6.142)/y + (6*t^7.189)/y + (8*t^7.953)/y - (10*t^8.237)/y - t^4.047*y - 4*t^6.142*y + 6*t^7.189*y + 8*t^7.953*y - 10*t^8.237*y	t^2.095/(g1*g2^3) + (g1*t^2.095)/(g2*g3^4) + (2*t^2.095)/(g2^2*g3^2) + g2^3*g3^3*t^2.858 + (g2^5*t^3.905)/g3 + (g2^4*g3*t^3.905)/g1 + g1*g3^3*t^3.905 + (g3^5*t^3.905)/g2 + t^4.189/(g1^2*g2^6) + (g1^2*t^4.189)/(g2^2*g3^8) + (2*g1*t^4.189)/(g2^3*g3^6) + (4*t^4.189)/(g2^4*g3^4) + (2*t^4.189)/(g1*g2^5*g3^2) + (g1*g2^2*t^4.953)/g3 + 3*g2*g3*t^4.953 + (g3^3*t^4.953)/g1 + g2^6*g3^6*t^5.716 - 3*t^6. + (g1*g2^4*t^6.)/g3^5 + (2*g2^3*t^6.)/g3^3 - (g1*g2*t^6.)/g3^2 + (g1^2*t^6.)/(g2*g3) + (2*g2^2*t^6.)/(g1*g3) + (2*g1*g3*t^6.)/g2^2 + (g2*g3*t^6.)/g1^2 - (g3^2*t^6.)/(g1*g2) + (2*g3^3*t^6.)/g2^3 + (g3^5*t^6.)/(g1*g2^4) + t^6.284/(g1^3*g2^9) + (g1^3*t^6.284)/(g2^3*g3^12) + (2*g1^2*t^6.284)/(g2^4*g3^10) + (4*g1*t^6.284)/(g2^5*g3^8) + (6*t^6.284)/(g2^6*g3^6) + (4*t^6.284)/(g1*g2^7*g3^4) + (2*t^6.284)/(g1^2*g2^8*g3^2) + g2^8*g3^2*t^6.763 + (g2^7*g3^4*t^6.763)/g1 + g1*g2^3*g3^6*t^6.763 + g2^2*g3^8*t^6.763 - (g1*t^7.047)/g2^3 + (g1^2*g2*t^7.047)/g3^5 - (g2^2*t^7.047)/g3^4 + (2*g1*t^7.047)/g3^3 - (g2*t^7.047)/(g1*g3^2) + (4*t^7.047)/(g2*g3) + (2*g3*t^7.047)/(g1*g2^2) - (g3^2*t^7.047)/g2^4 + (g3^3*t^7.047)/(g1^2*g2^3) + (g2^9*t^7.811)/g1 + (g2^10*t^7.811)/g3^2 - g2^7*g3*t^7.811 + g1*g2^5*g3^2*t^7.811 + (g2^8*g3^2*t^7.811)/g1^2 - (g2^6*g3^3*t^7.811)/g1 + 2*g2^4*g3^4*t^7.811 - g1*g2^2*g3^5*t^7.811 + g1^2*g3^6*t^7.811 + (g2^3*g3^6*t^7.811)/g1 - g2*g3^7*t^7.811 + (g1*g3^8*t^7.811)/g2 + (g3^10*t^7.811)/g2^2 - (5*t^8.095)/(g1*g2^3) + (g1^2*g2^3*t^8.095)/g3^9 + (2*g1*g2^2*t^8.095)/g3^7 - (g1^2*t^8.095)/g3^6 + (g1^3*t^8.095)/(g2^2*g3^5) + (3*g2*t^8.095)/g3^5 - (5*g1*t^8.095)/(g2*g3^4) + (3*t^8.095)/(g1*g3^3) + (2*g1^2*t^8.095)/(g2^3*g3^3) - (7*t^8.095)/(g2^2*g3^2) + (3*g1*t^8.095)/(g2^4*g3) + (2*t^8.095)/(g1^2*g2*g3) + (3*g3*t^8.095)/g2^5 + (g3*t^8.095)/(g1^3*g2^2) - (g3^2*t^8.095)/(g1^2*g2^4) + (2*g3^3*t^8.095)/(g1*g2^6) + (g3^5*t^8.095)/(g1^2*g2^7) + t^8.379/(g1^4*g2^12) + (g1^4*t^8.379)/(g2^4*g3^16) + (2*g1^3*t^8.379)/(g2^5*g3^14) + (4*g1^2*t^8.379)/(g2^6*g3^12) + (6*g1*t^8.379)/(g2^7*g3^10) + (9*t^8.379)/(g2^8*g3^8) + (6*t^8.379)/(g1*g2^9*g3^6) + (4*t^8.379)/(g1^2*g2^10*g3^4) + (2*t^8.379)/(g1^3*g2^11*g3^2) + g2^9*g3^9*t^8.574 + 2*g2^6*t^8.858 + (g1*g2^7*t^8.858)/g3^2 - 2*g1*g2^4*g3*t^8.858 + g1^2*g2^2*g3^2*t^8.858 + (2*g2^5*g3^2*t^8.858)/g1 - 5*g2^3*g3^3*t^8.858 + 2*g1*g2*g3^4*t^8.858 + (g2^4*g3^4*t^8.858)/g1^2 - (2*g2^2*g3^5*t^8.858)/g1 + 2*g3^6*t^8.858 + (g3^8*t^8.858)/(g1*g2) - t^4.047/(g2*g3*y) - (g1*t^6.142)/(g2^2*g3^5*y) - (2*t^6.142)/(g2^3*g3^3*y) - t^6.142/(g1*g2^4*g3*y) + (2*g1*t^7.189)/(g2^3*g3^6*y) + (2*t^7.189)/(g2^4*g3^4*y) + (2*t^7.189)/(g1*g2^5*g3^2*y) + (2*g1*g2^2*t^7.953)/(g3*y) + (4*g2*g3*t^7.953)/y + (2*g3^3*t^7.953)/(g1*y) - (g1^2*t^8.237)/(g2^3*g3^9*y) - (2*g1*t^8.237)/(g2^4*g3^7*y) - (4*t^8.237)/(g2^5*g3^5*y) - (2*t^8.237)/(g1*g2^6*g3^3*y) - t^8.237/(g1^2*g2^7*g3*y) - (t^4.047*y)/(g2*g3) - (g1*t^6.142*y)/(g2^2*g3^5) - (2*t^6.142*y)/(g2^3*g3^3) - (t^6.142*y)/(g1*g2^4*g3) + (2*g1*t^7.189*y)/(g2^3*g3^6) + (2*t^7.189*y)/(g2^4*g3^4) + (2*t^7.189*y)/(g1*g2^5*g3^2) + (2*g1*g2^2*t^7.953*y)/g3 + 4*g2*g3*t^7.953*y + (2*g3^3*t^7.953*y)/g1 - (g1^2*t^8.237*y)/(g2^3*g3^9) - (2*g1*t^8.237*y)/(g2^4*g3^7) - (4*t^8.237*y)/(g2^5*g3^5) - (2*t^8.237*y)/(g1*g2^6*g3^3) - (t^8.237*y)/(g1^2*g2^7*g3)

Deformation

Here is the data for the deformed fixed points from the chosen fixed point.

#	Superpotential	Central Charge $a$	Central Charge $c$	Ratio $a/c$	$R$-charges	Superconformal Index	More Info.	Rational

Equivalent Fixed Points from Other Seed Theories

Here is a list of equivalent fixed points from other gauge theories.

#	Theory	Superpotential	Central Charge $a$	Central Charge $c$	Ratio $a/c$	$R$-charges	Superconformal Index	More Info.	Rational

Equivalent Fixed Points from the Same Seed Theory

Below is a list of equivalent fixed points from the same seed theories.

id	Theory	Superpotential	Central Charge $a$	Central Charge $c$	Ratio $a/c$	$R$-charges	More Info.	Rational

Previous Theory

The previous fixed point before deforming to get the chosen fixed point.

#	Theory	Superpotential	Central Charge $a$	Central Charge $c$	Ratio $a/c$	$R$-charges	Superconformal Index	More Info.	Rational
45852	SU2adj1nf2	${}\phi_{1}q_{1}q_{2}$ + ${ }M_{1}\phi_{1}\tilde{q}_{1}\tilde{q}_{2}$ + ${ }M_{2}q_{2}\tilde{q}_{1}$	0.6485	0.7964	0.8143	[M:[0.7044, 0.6901], q:[0.8132, 0.8346], qb:[0.4753, 0.4681], phi:[0.3522]]	t^2.07 + 2*t^2.113 + t^2.83 + t^3.844 + 2*t^3.865 + 2*t^3.908 + t^4.141 + 2*t^4.184 + 3*t^4.226 + t^4.901 + 3*t^4.943 + t^5.66 + t^5.914 + 2*t^5.936 + t^5.957 + 4*t^5.979 - 3*t^6. - t^4.057/y - t^4.057*y	detail