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
5969	SU2adj1nf2	${}M_{1}q_{1}q_{2}$ + ${ }M_{2}\tilde{q}_{1}\tilde{q}_{2}$ + ${ }\phi_{1}q_{1}^{2}$ + ${ }M_{1}\phi_{1}^{2}$ + ${ }M_{2}M_{3}$ + ${ }M_{4}\phi_{1}q_{2}\tilde{q}_{1}$ + ${ }M_{4}\phi_{1}q_{2}^{2}$ + ${ }M_{5}\phi_{1}q_{2}\tilde{q}_{2}$ + ${ }M_{6}\phi_{1}q_{2}^{2}$ + ${ }M_{7}q_{1}\tilde{q}_{2}$ + ${ }M_{8}\phi_{1}\tilde{q}_{1}^{2}$ + ${ }M_{9}\phi_{1}\tilde{q}_{1}\tilde{q}_{2}$	0.6961	0.9605	0.7247	[M:[0.9228, 1.2315, 0.7685, 0.7685, 0.6929, 0.7685, 0.8473, 0.7685, 0.6929], q:[0.7307, 0.3465], qb:[0.3465, 0.422], phi:[0.5386]]	[M:[[4], [-12], [12], [12], [-10], [12], [-18], [12], [-10]], q:[[1], [-5]], qb:[[-5], [17]], phi:[[-2]]]	1

Relevant Operators	Marginal Operators	$n_{marginal}$$-$$|F_{IR}|$	Superconformal Index	Refined index
${}M_{5}$, ${ }M_{9}$, ${ }q_{2}\tilde{q}_{1}$, ${ }M_{3}$, ${ }M_{4}$, ${ }M_{6}$, ${ }M_{8}$, ${ }q_{2}\tilde{q}_{2}$, ${ }M_{7}$, ${ }M_{1}$, ${ }\phi_{1}^{2}$, ${ }q_{1}\tilde{q}_{1}$, ${ }\phi_{1}\tilde{q}_{2}^{2}$, ${ }M_{5}^{2}$, ${ }M_{5}M_{9}$, ${ }M_{9}^{2}$, ${ }M_{5}q_{2}\tilde{q}_{1}$, ${ }M_{9}q_{2}\tilde{q}_{1}$, ${ }q_{2}^{2}\tilde{q}_{1}^{2}$, ${ }M_{3}M_{5}$, ${ }M_{4}M_{5}$, ${ }M_{5}M_{6}$, ${ }M_{5}M_{8}$, ${ }M_{3}M_{9}$, ${ }M_{4}M_{9}$, ${ }M_{6}M_{9}$, ${ }M_{8}M_{9}$, ${ }M_{3}q_{2}\tilde{q}_{1}$, ${ }M_{4}q_{2}\tilde{q}_{1}$, ${ }M_{6}q_{2}\tilde{q}_{1}$, ${ }M_{8}q_{2}\tilde{q}_{1}$, ${ }M_{5}q_{2}\tilde{q}_{2}$, ${ }M_{9}q_{2}\tilde{q}_{2}$, ${ }q_{2}^{2}\tilde{q}_{1}\tilde{q}_{2}$, ${ }M_{3}^{2}$, ${ }M_{3}M_{4}$, ${ }M_{4}^{2}$, ${ }M_{3}M_{6}$, ${ }M_{4}M_{6}$, ${ }M_{6}^{2}$, ${ }M_{3}M_{8}$, ${ }M_{4}M_{8}$, ${ }M_{6}M_{8}$, ${ }M_{8}^{2}$, ${ }M_{3}q_{2}\tilde{q}_{2}$, ${ }M_{4}q_{2}\tilde{q}_{2}$, ${ }M_{6}q_{2}\tilde{q}_{2}$, ${ }M_{8}q_{2}\tilde{q}_{2}$, ${ }q_{2}^{2}\tilde{q}_{2}^{2}$, ${ }M_{5}M_{7}$, ${ }M_{7}M_{9}$, ${ }M_{7}q_{2}\tilde{q}_{1}$, ${ }M_{1}M_{5}$, ${ }M_{3}M_{7}$, ${ }M_{4}M_{7}$, ${ }M_{6}M_{7}$, ${ }M_{7}M_{8}$, ${ }M_{1}M_{9}$, ${ }\phi_{1}q_{1}q_{2}$, ${ }\phi_{1}q_{1}\tilde{q}_{1}$, ${ }M_{7}q_{2}\tilde{q}_{2}$, ${ }M_{1}M_{3}$, ${ }M_{1}M_{4}$, ${ }M_{1}M_{6}$, ${ }M_{1}M_{8}$, ${ }\phi_{1}q_{1}\tilde{q}_{2}$, ${ }M_{7}^{2}$, ${ }M_{1}M_{7}$, ${ }M_{5}\phi_{1}^{2}$, ${ }M_{9}\phi_{1}^{2}$, ${ }M_{5}q_{1}\tilde{q}_{1}$, ${ }M_{9}q_{1}\tilde{q}_{1}$, ${ }\phi_{1}^{2}q_{2}\tilde{q}_{1}$, ${ }q_{1}q_{2}\tilde{q}_{1}^{2}$, ${ }M_{1}^{2}$, ${ }M_{3}\phi_{1}^{2}$, ${ }M_{4}\phi_{1}^{2}$, ${ }M_{6}\phi_{1}^{2}$, ${ }M_{8}\phi_{1}^{2}$, ${ }M_{3}q_{1}\tilde{q}_{1}$, ${ }M_{4}q_{1}\tilde{q}_{1}$, ${ }M_{6}q_{1}\tilde{q}_{1}$, ${ }M_{8}q_{1}\tilde{q}_{1}$, ${ }\phi_{1}^{2}q_{2}\tilde{q}_{2}$	${}$	-5	3*t^2.079 + 5*t^2.305 + t^2.542 + t^2.768 + 2*t^3.232 + t^4.148 + 6*t^4.158 + 15*t^4.384 + 15*t^4.611 + 3*t^4.621 + 8*t^4.847 + 5*t^5.074 + t^5.084 + 7*t^5.31 + 10*t^5.537 - 5*t^6. + 10*t^6.237 + 5*t^6.453 + 28*t^6.463 + 43*t^6.69 + 6*t^6.7 + 35*t^6.916 + 18*t^6.926 + 24*t^7.153 + 3*t^7.163 + 15*t^7.379 + 17*t^7.389 + 27*t^7.616 + t^7.626 + 24*t^7.842 + t^7.852 - 15*t^8.079 + t^8.295 - 28*t^8.305 + 15*t^8.315 + 37*t^8.542 + 15*t^8.758 + 66*t^8.768 + 10*t^8.778 + 93*t^8.995 - t^4.616/y - (2*t^6.695)/y - (3*t^6.921)/y + (2*t^7.158)/y + (15*t^7.384)/y + (10*t^7.611)/y + (3*t^7.621)/y + (8*t^7.847)/y + (6*t^8.074)/y + (10*t^8.31)/y + (12*t^8.537)/y - t^8.773/y - t^4.616*y - 2*t^6.695*y - 3*t^6.921*y + 2*t^7.158*y + 15*t^7.384*y + 10*t^7.611*y + 3*t^7.621*y + 8*t^7.847*y + 6*t^8.074*y + 10*t^8.31*y + 12*t^8.537*y - t^8.773*y	(3*t^2.079)/g1^10 + 5*g1^12*t^2.305 + t^2.542/g1^18 + g1^4*t^2.768 + (2*t^3.232)/g1^4 + g1^32*t^4.148 + (6*t^4.158)/g1^20 + 15*g1^2*t^4.384 + 15*g1^24*t^4.611 + (3*t^4.621)/g1^28 + (8*t^4.847)/g1^6 + 5*g1^16*t^5.074 + t^5.084/g1^36 + (7*t^5.31)/g1^14 + 10*g1^8*t^5.537 - 5*t^6. + (10*t^6.237)/g1^30 + 5*g1^44*t^6.453 + (28*t^6.463)/g1^8 + 43*g1^14*t^6.69 + (6*t^6.7)/g1^38 + 35*g1^36*t^6.916 + (18*t^6.926)/g1^16 + 24*g1^6*t^7.153 + (3*t^7.163)/g1^46 + 15*g1^28*t^7.379 + (17*t^7.389)/g1^24 + (27*t^7.616)/g1^2 + t^7.626/g1^54 + 24*g1^20*t^7.842 + t^7.852/g1^32 - (15*t^8.079)/g1^10 + g1^64*t^8.295 - 28*g1^12*t^8.305 + (15*t^8.315)/g1^40 + (37*t^8.542)/g1^18 + 15*g1^56*t^8.758 + 66*g1^4*t^8.768 + (10*t^8.778)/g1^48 + 93*g1^26*t^8.995 - t^4.616/(g1^2*y) - (2*t^6.695)/(g1^12*y) - (3*g1^10*t^6.921)/y + (2*t^7.158)/(g1^20*y) + (15*g1^2*t^7.384)/y + (10*g1^24*t^7.611)/y + (3*t^7.621)/(g1^28*y) + (8*t^7.847)/(g1^6*y) + (6*g1^16*t^8.074)/y + (10*t^8.31)/(g1^14*y) + (12*g1^8*t^8.537)/y - t^8.773/(g1^22*y) - (t^4.616*y)/g1^2 - (2*t^6.695*y)/g1^12 - 3*g1^10*t^6.921*y + (2*t^7.158*y)/g1^20 + 15*g1^2*t^7.384*y + 10*g1^24*t^7.611*y + (3*t^7.621*y)/g1^28 + (8*t^7.847*y)/g1^6 + 6*g1^16*t^8.074*y + (10*t^8.31*y)/g1^14 + 12*g1^8*t^8.537*y - (t^8.773*y)/g1^22

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
4463	SU2adj1nf2	${}M_{1}q_{1}q_{2}$ + ${ }M_{2}\tilde{q}_{1}\tilde{q}_{2}$ + ${ }\phi_{1}q_{1}^{2}$ + ${ }M_{1}\phi_{1}^{2}$ + ${ }M_{2}M_{3}$ + ${ }M_{4}\phi_{1}q_{2}\tilde{q}_{1}$ + ${ }M_{4}\phi_{1}q_{2}^{2}$ + ${ }M_{5}\phi_{1}q_{2}\tilde{q}_{2}$ + ${ }M_{6}\phi_{1}q_{2}^{2}$ + ${ }M_{7}q_{1}\tilde{q}_{2}$ + ${ }M_{8}\phi_{1}\tilde{q}_{1}^{2}$	0.6754	0.9209	0.7334	[M:[0.9222, 1.2333, 0.7667, 0.7667, 0.6944, 0.7667, 0.8499, 0.7667], q:[0.7306, 0.3472], qb:[0.3472, 0.4196], phi:[0.5389]]	2*t^2.083 + 5*t^2.3 + t^2.55 + t^2.767 + 2*t^3.233 + t^3.917 + t^4.134 + 3*t^4.166 + 10*t^4.383 + 15*t^4.6 + 2*t^4.633 + 7*t^4.85 + 5*t^5.067 + t^5.099 + 5*t^5.316 + 10*t^5.533 - 3*t^6. - t^4.617/y - t^4.617*y	detail